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JEE MAIN 2024
04-04-2024 S1
Question
Let a unit vector which makes an angle of $60^{\circ}$ with $2 \hat{\imath}+2 \hat{\jmath}-\hat{k}$ and an angle of $45^{\circ}$ with $\hat{\imath}-\hat{k}$ be $\vec{C}$. Then $\vec{C}+\left(-\frac{1}{2} \hat{\imath}+\frac{1}{3 \sqrt{2}} \hat{\jmath}-\frac{\sqrt{2}}{3} \hat{k}\right)$ is :
Select the correct option:
A
$-\frac{\sqrt{2}}{3} \hat{\imath}+\frac{\sqrt{2}}{3} \hat{\jmath}+\left(\frac{1}{2}+\frac{2 \sqrt{2}}{3}\right) \hat{k}$
B
$\frac{\sqrt{2}}{3} \hat{\imath}+\frac{1}{3 \sqrt{2}} \hat{\jmath}-\frac{1}{2} \hat{k}$
C
$\left(\frac{1}{\sqrt{3}}+\frac{1}{2}\right) \hat{\imath}+\left(\frac{1}{\sqrt{3}}-\frac{1}{3 \sqrt{2}}\right) \hat{\jmath}+\left(\frac{1}{\sqrt{3}}+\frac{\sqrt{2}}{3}\right) \hat{k}$
D
$\frac{\sqrt{2}}{3} \hat{\imath}-\frac{1}{2} \hat{k}$
✓ Correct! Well done.
✗ Incorrect. Try again or view the solution.
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