A unit vector in the direction of resultant vector of A = -2i + 3j + k and B = i + 2j - 4k is (a) (-3i + j + 5k)/(√(35)) (b) (i + 2j - 4k)/(√(35)) (c) (-2i + 3j + k)/(√(35)) (d) (-i + 5j - 3k)/(√(35))

Answer: (d). A + B = (-2 + 1)i + (3 + 2)j + (1 - 4)k = -i + 5j - 3k Magnitude = √(1 + 25 + 9) = √(35) So the answer is (d) (-i + 5j - 3k)/(√(35)).

A unit vector in the direction of resultant vector of A = -2i + 3j +… | MHT CET 2025 (21 Apr, Shift 2)

Q9MHT CET 2025 · 21 APR · SHIFT 2Medium

Vector Basics, Unit Vectors & Components

A unit vector in the direction of resultant vector of $\vec{A} = -2\hat{i} + 3\hat{j} + \hat{k}$ and $\vec{B} = \hat{i} + 2\hat{j} - 4\hat{k}$ is

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Answer: (d)

$\vec{A} + \vec{B} = (-2 + 1)\hat{i} + (3 + 2)\hat{j} + (1 - 4)\hat{k} = -\hat{i} + 5\hat{j} - 3\hat{k}$
Magnitude $= \sqrt{1 + 25 + 9} = \sqrt{35}$
So the answer is (d) $\frac{-\hat{i} + 5\hat{j} - 3\hat{k}}{\sqrt{35}}$ .

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