Three vectors are expressed as a = 4i - j, b = -3i + 2j and c = -k. The unit vector along the direction of sum of these vectors is (a) (i + j - k)/(√(3)) (b) 1/3(i - j + k) (c) 1/√(2)(i - j + k) (d) 1/√(2)(i + j + k)

Answer: (a). a + b + c = (4 - 3)i + (-1 + 2)j - k = i + j - k Magnitude = √(1 + 1 + 1) = √(3) Unit vector = (i + j - k)/(√(3)) So the answer is (a).

Three vectors are expressed as a = 4i - j, b = -3i + 2j and c = -k… | MHT CET 2025 (20 Apr, Shift 2)

Q8MHT CET 2025 · 20 APR · SHIFT 2Easy

Vector Basics, Unit Vectors & Components

Three vectors are expressed as $\vec{a} = 4\hat{i} - \hat{j}, \vec{b} = -3\hat{i} + 2\hat{j}$ and $\vec{c} = -\hat{k}$ . The unit vector along the direction of sum of these vectors is

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Answer: (a)

$\vec{a} + \vec{b} + \vec{c} = (4 - 3)\hat{i} + (-1 + 2)\hat{j} - \hat{k} = \hat{i} + \hat{j} - \hat{k}$
Magnitude $= \sqrt{1 + 1 + 1} = \sqrt{3}$
Unit vector $= \frac{\hat{i} + \hat{j} - \hat{k}}{\sqrt{3}}$
So the answer is (a).

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