Q1 MHT CET 2026 · 17 APR · SHIFT 2 Easy ☆
Vector Basics, Unit Vectors & Components · Types of vectors & vector laws
There are two vectors A ⃗ = 6 i ^ + 9 j ^ − k ^ \vec{A} = 6\hat{i} + 9\hat{j} - \hat{k} A = 6 i ^ + 9 j ^ − k ^ B ⃗ = 2 i ^ + 3 j ^ − p k ^ \vec{B} = 2\hat{i} + 3\hat{j} - p\hat{k} B = 2 i ^ + 3 j ^ − p k ^
(a) 3 3 3 (b) 1 3 \frac{1}{3} 3 1 (c) 2 3 \frac{2}{3} 3 2 (d) − 1 3 -\frac{1}{3} − 3 1 Show answer and solution
Answer: (b)
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Report a mistake Q2 MHT CET 2026 · 15 APR · SHIFT 2 Easy ☆
Vector Basics, Unit Vectors & Components · Types of vectors & vector laws
Let A ⃗ \vec{A} A B ⃗ \vec{B} B
(a) A ⃗ ⋅ B ⃗ = − B ⃗ ⋅ A ⃗ \vec{A} \cdot \vec{B} = -\vec{B} \cdot \vec{A} A ⋅ B = − B ⋅ A (b) A ⃗ × B ⃗ = B ⃗ × A ⃗ \vec{A} \times \vec{B} = \vec{B} \times \vec{A} A × B = B × A (c) A ⃗ + B ⃗ = B ⃗ + A ⃗ \vec{A} + \vec{B} = \vec{B} + \vec{A} A + B = B + A (d) A ⃗ − B ⃗ = B ⃗ − A ⃗ \vec{A} - \vec{B} = \vec{B} - \vec{A} A − B = B − A Show answer and solution
Answer: (c)
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Report a mistake Q3 MHT CET 2026 · 18 APR · SHIFT 2 Easy ☆
Vector Basics, Unit Vectors & Components · Unit vector & magnitude
If a unit vector is represented by U ⃗ = 0.9 i ^ − 0.2 j ^ + m k ^ \vec{U} = 0.9\hat{i} - 0.2\hat{j} + m\hat{k} U = 0.9 i ^ − 0.2 j ^ + m k ^
(a) 0.85 0.85 0.85 (b) 0.15 \sqrt{0.15} 0.15 (c) 1 1 1 (d) 0.77 \sqrt{0.77} 0.77 Show answer and solution
Answer: (b)
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Report a mistake Q4 MHT CET 2026 · 15 APR · SHIFT 1 Easy ☆
Vector Basics, Unit Vectors & Components · Unit vector & magnitude
A vector A ⃗ \vec{A} A ( i ^ − 2 j ^ + 2 k ^ ) (\hat{i} - 2\hat{j} + 2\hat{k}) ( i ^ − 2 j ^ + 2 k ^ ) ( − 2 i ^ + j ^ − k ^ ) (-2\hat{i} + \hat{j} - \hat{k}) ( − 2 i ^ + j ^ − k ^ ) A ⃗ \vec{A} A
(a) 3 \sqrt{3} 3 (b) 6 \sqrt{6} 6 (c) 8 \sqrt{8} 8 (d) 10 \sqrt{10} 10 Show answer and solution
Answer: (b)
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Report a mistake Q5 MHT CET 2026 · 15 MAY · SHIFT 2 Easy ☆
Vector Basics, Unit Vectors & Components · Components & direction cosines
The angle made by a vector B ⃗ = 3 i ^ + 2 j ^ + 4 k ^ \vec{B} = 3\hat{i} + 2\hat{j} + 4\hat{k} B = 3 i ^ + 2 j ^ + 4 k ^
(a) cos − 1 ( 4 11 ) \cos^{-1}\left(\frac{4}{\sqrt{11}}\right) cos − 1 ( 11 4 ) (b) cos − 1 ( 3 17 ) \cos^{-1}\left(\frac{3}{\sqrt{17}}\right) cos − 1 ( 17 3 ) (c) cos − 1 ( 2 29 ) \cos^{-1}\left(\frac{2}{\sqrt{29}}\right) cos − 1 ( 29 2 ) (d) cos − 1 ( 5 23 ) \cos^{-1}\left(\frac{5}{\sqrt{23}}\right) cos − 1 ( 23 5 ) Show answer and solution
Answer: (c)
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Report a mistake Q6 MHT CET 2026 · 18 APR · SHIFT 1 Easy ☆
Vector Basics, Unit Vectors & Components · Components & direction cosines
The angle made by vector A ⃗ = 2 i ^ + 3 j ^ \vec{A} = 2\hat{i} + 3\hat{j} A = 2 i ^ + 3 j ^
(a) tan − 1 2 13 tan − 1 3 13 \tan^{-1} 2\sqrt{13} \quad \tan^{-1} 3\sqrt{13} tan − 1 2 13 tan − 1 3 13 (b) cos − 1 2 13 cos − 1 3 13 \cos^{-1}\frac{2}{\sqrt{13}} \quad \cos^{-1}\frac{3}{\sqrt{13}} cos − 1 13 2 cos − 1 13 3 (c) cos − 1 1 2 cos − 1 1 3 \cos^{-1}\frac{1}{\sqrt{2}} \quad \cos^{-1}\frac{1}{\sqrt{3}} cos − 1 2 1 cos − 1 3 1 (d) sin − 1 1 6 sin − 1 1 2 3 \sin^{-1}\frac{1}{\sqrt{6}} \quad \sin^{-1}\frac{1}{2\sqrt{3}} sin − 1 6 1 sin − 1 2 3 1 Show answer and solution
Answer: (b)
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Report a mistake Q7 JEE Main 2026 · 2 APR · SHIFT 1 Medium ☆
Vector Basics, Unit Vectors & Components · Components & direction cosines
The velocity of a particle is given as v ⃗ = − x i ^ + 2 y j ^ − z k ^ \vec{v} = -x\hat{i} + 2y\hat{j} - z\hat{k} v = − x i ^ + 2 y j ^ − z k ^
(a) 6 \sqrt{6} 6 (b) 9 9 9 (c) 33 \sqrt{33} 33 (d) 0 0 0 Show answer and solution
Answer: (b)
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Report a mistake Q8 MHT CET 2025 · 20 APR · SHIFT 2 Easy ☆
Vector Basics, Unit Vectors & Components · Unit vector & magnitude
Three vectors are expressed as a ⃗ = 4 i ^ − j ^ , b ⃗ = − 3 i ^ + 2 j ^ \vec{a} = 4\hat{i} - \hat{j}, \vec{b} = -3\hat{i} + 2\hat{j} a = 4 i ^ − j ^ , b = − 3 i ^ + 2 j ^ c ⃗ = − k ^ \vec{c} = -\hat{k} c = − k ^
(a) i ^ + j ^ − k ^ 3 \frac{\hat{i} + \hat{j} - \hat{k}}{\sqrt{3}} 3 i ^ + j ^ − k ^ (b) 1 3 ( i ^ − j ^ + k ^ ) \frac{1}{3}(\hat{i} - \hat{j} + \hat{k}) 3 1 ( i ^ − j ^ + k ^ ) (c) 1 2 ( i ^ − j ^ + k ^ ) \frac{1}{\sqrt{2}}(\hat{i} - \hat{j} + \hat{k}) 2 1 ( i ^ − j ^ + k ^ ) (d) 1 2 ( i ^ + j ^ + k ^ ) \frac{1}{\sqrt{2}}(\hat{i} + \hat{j} + \hat{k}) 2 1 ( i ^ + j ^ + k ^ ) Show answer and solution
Answer: (a)
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Report a mistake Q9 MHT CET 2025 · 21 APR · SHIFT 2 Medium ☆
Vector Basics, Unit Vectors & Components · Unit vector & magnitude
A unit vector in the direction of resultant vector of A ⃗ = − 2 i ^ + 3 j ^ + k ^ \vec{A} = -2\hat{i} + 3\hat{j} + \hat{k} A = − 2 i ^ + 3 j ^ + k ^ B ⃗ = i ^ + 2 j ^ − 4 k ^ \vec{B} = \hat{i} + 2\hat{j} - 4\hat{k} B = i ^ + 2 j ^ − 4 k ^
(a) − 3 i ^ + j ^ + 5 k ^ 35 \frac{-3\hat{i} + \hat{j} + 5\hat{k}}{\sqrt{35}} 35 − 3 i ^ + j ^ + 5 k ^ (b) i ^ + 2 j ^ − 4 k ^ 35 \frac{\hat{i} + 2\hat{j} - 4\hat{k}}{\sqrt{35}} 35 i ^ + 2 j ^ − 4 k ^ (c) − 2 i ^ + 3 j ^ + k ^ 35 \frac{-2\hat{i} + 3\hat{j} + \hat{k}}{\sqrt{35}} 35 − 2 i ^ + 3 j ^ + k ^ (d) − i ^ + 5 j ^ − 3 k ^ 35 \frac{-\hat{i} + 5\hat{j} - 3\hat{k}}{\sqrt{35}} 35 − i ^ + 5 j ^ − 3 k ^ Show answer and solution
Answer: (d)
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Report a mistake Q10 JEE Main 2024 · 30 JAN · SHIFT 2 Medium ☆
Vector Basics, Unit Vectors & Components · Unit vector & magnitude
A vector has magnitude same as that of A ⃗ = 3 i ^ + 4 j ^ \vec{A} = 3\hat{i} + 4\hat{j} A = 3 i ^ + 4 j ^ B ⃗ = 4 i ^ + 3 j ^ \vec{B} = 4\hat{i} + 3\hat{j} B = 4 i ^ + 3 j ^ x x x y y y x x x x = x = x =
Numerical answer type. Work it out, then open the answer.
Show answer and solution
Answer: 4
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Report a mistake Q11 JEE Main 2024 · 8 APR · SHIFT 1 Medium ☆
Vector Basics, Unit Vectors & Components · Components & direction cosines
Three vectors O P → , O Q → \overrightarrow{OP}, \overrightarrow{OQ} OP , OQ O R → \overrightarrow{OR} OR A A A A x A\sqrt{x} A x x x x
Numerical answer type. Work it out, then open the answer.
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Answer: 3
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Report a mistake Q12 JEE Main 2023 · 11 APR · SHIFT 2 Easy ☆
Vector Basics, Unit Vectors & Components · Unit vector & magnitude
When vector A ⃗ = 2 i ^ + 3 j ^ + 2 k ^ \vec{A} = 2\hat{i} + 3\hat{j} + 2\hat{k} A = 2 i ^ + 3 j ^ + 2 k ^ B ⃗ \vec{B} B 2 j ^ 2\hat{j} 2 j ^ B ⃗ \vec{B} B
(a) 3 (b) 33 \sqrt{33} 33 (c) 6 \sqrt{6} 6 (d) 5 \sqrt{5} 5 Show answer and solution
Answer: (b)
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Report a mistake Q13 JEE Main 2023 · 15 APR · SHIFT 1 Easy ☆
Vector Basics, Unit Vectors & Components · Components & direction cosines
A vector in x − y x - y x − y 3 0 ∘ 30^\circ 3 0 ∘ y y y y y y 2 3 2\sqrt{3} 2 3 x x x
(a) 3 \sqrt{3} 3 (b) 2 (c) 6 (d) 1 3 \frac{1}{\sqrt{3}} 3 1 Show answer and solution
Answer: (b)
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Report a mistake Q14 JEE Main 2021 · 27 AUG · SHIFT 1 Medium ☆
Vector Basics, Unit Vectors & Components · Components & direction cosines
The resultant of these forces O P → , O Q → , O R → , O S → \overrightarrow{OP}, \overrightarrow{OQ}, \overrightarrow{OR}, \overrightarrow{OS} OP , OQ , OR , OS O T → \overrightarrow{OT} OT 3 = 1.7 , 2 = 1.4 \sqrt{3} = 1.7,\ \sqrt{2} = 1.4 3 = 1.7 , 2 = 1.4 i ^ \hat{i} i ^ j ^ \hat{j} j ^
(a) 9.25 i ^ + 5 j ^ 9.25\hat{i} + 5\hat{j} 9.25 i ^ + 5 j ^ (b) 3 i ^ + 15 j ^ 3\hat{i} + 15\hat{j} 3 i ^ + 15 j ^ (c) 2.5 i ^ − 14.5 j ^ 2.5\hat{i} - 14.5\hat{j} 2.5 i ^ − 14.5 j ^ (d) − 1.5 i ^ − 15.5 j ^ -1.5\hat{i} - 15.5\hat{j} − 1.5 i ^ − 15.5 j ^ Show answer and solution
Answer: (a)
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Report a mistake Q15 JEE Main 2021 · 26 AUG · SHIFT 1 Medium ☆
Vector Basics, Unit Vectors & Components · Components & direction cosines
The magnitude of vectors O A → O B → \overrightarrow{OA} \ \overrightarrow{OB} O A OB O C → \overrightarrow{OC} OC O A → + O B → − O C → \overrightarrow{OA} + \overrightarrow{OB} - \overrightarrow{OC} O A + OB − OC
(a) tan − 1 ( 1 − 3 − 2 ) ( 1 + 3 + 2 ) \tan^{-1}\frac{(1-\sqrt{3}-\sqrt{2})}{(1+\sqrt{3}+\sqrt{2})} tan − 1 ( 1 + 3 + 2 ) ( 1 − 3 − 2 ) (b) tan − 1 ( 3 − 1 + 2 ) ( 1 + 3 − 2 ) \tan^{-1}\frac{(\sqrt{3}-1+\sqrt{2})}{(1+\sqrt{3}-\sqrt{2})} tan − 1 ( 1 + 3 − 2 ) ( 3 − 1 + 2 ) (c) tan − 1 ( 3 − 1 + 2 ) ( 1 − 3 + 2 ) \tan^{-1}\frac{(\sqrt{3}-1+\sqrt{2})}{(1-\sqrt{3}+\sqrt{2})} tan − 1 ( 1 − 3 + 2 ) ( 3 − 1 + 2 ) (d) tan − 1 ( 1 + 3 − 2 ) ( 1 − 3 − 2 ) \tan^{-1}\frac{(1+\sqrt{3}-\sqrt{2})}{(1-\sqrt{3}-\sqrt{2})} tan − 1 ( 1 − 3 − 2 ) ( 1 + 3 − 2 ) Show answer and solution
Answer: (a)
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Report a mistake Q16 MHT CET 2020 · 19 OCT · SHIFT 2 Easy ☆
Vector Basics, Unit Vectors & Components · Components & direction cosines
The angle subtended by the vector A = 4 i ^ + 3 j ^ + 12 k ^ A = 4\hat{i} + 3\hat{j} + 12\hat{k} A = 4 i ^ + 3 j ^ + 12 k ^ X X X
(a) cos − 1 ( 3 13 ) \cos^{-1}\left(\frac{3}{13}\right) cos − 1 ( 13 3 ) (b) sin − 1 ( 3 13 ) \sin^{-1}\left(\frac{3}{13}\right) sin − 1 ( 13 3 ) (c) sin − 1 ( 4 13 ) \sin^{-1}\left(\frac{4}{13}\right) sin − 1 ( 13 4 ) (d) cos − 1 ( 4 13 ) \cos^{-1}\left(\frac{4}{13}\right) cos − 1 ( 13 4 ) Show answer and solution
Answer: (d)
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Report a mistake Q17 MHT CET 2020 · 16 OCT · SHIFT 2 Easy ☆
Vector Basics, Unit Vectors & Components · Components & direction cosines
The x , y x, y x , y P \mathbf{P} P x , y x, y x , y P \mathbf{P} P Q \mathbf{Q} Q Q \mathbf{Q} Q
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Answer: (a)
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Report a mistake Q18 MHT CET 2019 · 3 MAY · SHIFT 1 Easy ☆
Vector Basics, Unit Vectors & Components · Components & direction cosines
A vector P P P X X X Y Y Y Q Q Q X X X ( Q − P ) (\mathbf{Q} - \mathbf{P}) ( Q − P )
(a) 4 ( 2 i ^ − j ^ ) 4(2\hat{i} - \hat{j}) 4 ( 2 i ^ − j ^ ) (b) − 4 ( 2 i ^ − j ^ ) -4(2\hat{i} - \hat{j}) − 4 ( 2 i ^ − j ^ ) (c) 4 ( 2 i ^ + j ^ ) 4(2\hat{i} + \hat{j}) 4 ( 2 i ^ + j ^ ) (d) − 4 ( 2 i ^ + j ^ ) -4(2\hat{i} + \hat{j}) − 4 ( 2 i ^ + j ^ ) Show answer and solution
Answer: (d)
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Report a mistake Q19 JEE Main 2019 · 10 JAN · SHIFT 1 Medium ☆
Vector Basics, Unit Vectors & Components · Components & direction cosines
In the cube of side ‘a’ shown in the figure, the vector from the central point of the face ABOD to the central point of the face BEFO will be -
(a) 1 2 a ( k ^ − i ^ ) \frac{1}{2}a\left(\hat{k} - \hat{i}\right) 2 1 a ( k ^ − i ^ ) (b) 1 2 a ( j ^ − i ^ ) \frac{1}{2}a\left(\hat{j} - \hat{i}\right) 2 1 a ( j ^ − i ^ ) (c) 1 2 a ( j ^ − k ^ ) \frac{1}{2}a\left(\hat{j} - \hat{k}\right) 2 1 a ( j ^ − k ^ ) (d) 1 2 a ( i ^ − k ^ ) \frac{1}{2}a\left(\hat{i} - \hat{k}\right) 2 1 a ( i ^ − k ^ ) Show answer and solution
Answer: (b)
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Report a mistake Q20 NEET 1999 · AIPMT Easy ☆
Vector Basics, Unit Vectors & Components · Unit vector & magnitude
If a unit vector is represented by 0.5 i ^ + 0.8 j ^ + c k ^ 0.5\hat{i} + 0.8\hat{j} + c\hat{k} 0.5 i ^ + 0.8 j ^ + c k ^ c c c
(a) 1 1 1 (b) 0.11 \sqrt{0.11} 0.11 (c) 0.01 \sqrt{0.01} 0.01 (d) 0.39 0.39 0.39 Show answer and solution
Answer: (b)
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