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Vector Algebra question

2024 · 4 Apr · Shift 1 · Q38

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JEE Main
Mathematics
Vector Algebra
2024 · 4 Apr · Shift 1 · Q38

Vector Algebra question

2024 · 4 Apr · Shift 1 · Q38

JEE MainMathematicsVector AlgebraMCQ+4 / −1

Let a unit vector which makes an angle of

60^{\circ}

with

2 \hat{i}+2 \hat{j}-\hat{k}

and an angle of

45^{\circ}

with

\hat{i}-\hat{k}

be

\vec{C}

. Then

\vec{C}+\left(-\frac{1}{2} \hat{i}+\frac{1}{3 \sqrt{2}} \hat{j}-\frac{\sqrt{2}}{3} \hat{k}\right)

is:

A
$-\frac{\sqrt{2}}{3} \hat{i}+\frac{\sqrt{2}}{3} \hat{j}+\left(\frac{1}{2}+\frac{2 \sqrt{2}}{3}\right) \hat{k}$
B
$\left(\frac{1}{\sqrt{3}}+\frac{1}{2}\right) \hat{i}+\left(\frac{1}{\sqrt{3}}-\frac{1}{3 \sqrt{2}}\right) \hat{j}+\left(\frac{1}{\sqrt{3}}+\frac{\sqrt{2}}{3}\right) \hat{k}$
C
$\frac{\sqrt{2}}{3} \hat{i}-\frac{1}{2} \hat{k}$
D
$\frac{\sqrt{2}}{3} \hat{i}+\frac{1}{3 \sqrt{2}} \hat{j}-\frac{1}{2} \hat{k}$

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