The resultant of two vectors A and B is C. If the magnitude of B is doubled, the new resultant vector becomes perpendicular to A, then the magnitude of C is (a) 4 B (b) 3 B (c) B (d) 2 B

Answer: (c). (A + 2B) · A = 0 ⇒ A² + 2ABcos θ = 0 C² = A² + B² + 2ABcos θ = B² ⇒ C = B So the answer is (c) B.

The resultant of two vectors A and B is C. If the magnitude of B is… | MHT CET 2025 (19 Apr, Shift 2)

Q7MHT CET 2025 · 19 APR · SHIFT 2Medium

Addition & Subtraction of Vectors

The resultant of two vectors $\vec{A}$ and $\vec{B}$ is $\vec{C}$ . If the magnitude of $\vec{B}$ is doubled, the new resultant vector becomes perpendicular to $\vec{A}$ , then the magnitude of $\vec{C}$ is

Show answer and solution

Answer: (c)

$(\vec{A} + 2\vec{B}) \cdot \vec{A} = 0 \Rightarrow A^2 + 2AB\cos\theta = 0$
$C^2 = A^2 + B^2 + 2AB\cos\theta = B^2 \Rightarrow C = B$
So the answer is (c) B.

Report a mistake

More questions on Addition & Subtraction of Vectors

The three vector A = 3i - 2j + k, B = i - 3j + 5k and C = 2i - j + 4k will formMHT CET 2025 (21 Apr, Shift 1)
The angle between vector Q and the resultant of (2Q + 2P) and (2Q - 2P) is:JEE Main 2024 (5 Apr, Shift 1)
If two vectors A and B having equal magnitude R are inclined at angle θ, thenJEE Main 2024 (31 Jan, Shift 2)
The resultant of two vectors A and B is perpendicular to A and its magnitude is half that…JEE Main 2024 (9 Apr, Shift 2)
If a and b make an angle cos ⁻¹(5/9) with each other, then |a + b| = √(2)|a - b| for |a|…JEE Main 2024 (9 Apr, Shift 1)
Two forces F₁ and F₂ are acting on a body. One force has magnitude thrice that of the…JEE Main 2024 (4 Apr, Shift 1)
Two forces having magnitude A and A/2 are perpendicular to each other. The magnitude of…JEE Main 2023 (8 Apr, Shift 1)
Two vectors A and B have equal magnitudes. If magnitude of A + B is equal to two times…JEE Main 2022 (29 Jun, Shift 1)

Addition & Subtraction of Vectors question from MHT CET 2025 (19 Apr, Shift 2)

More questions on Addition & Subtraction of Vectors