JEE Main 2024 (4 Apr, Shift 1) Maths Q18: Dot Product

Question

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 :

Accepted Answer

Option 3: $\frac{\sqrt{2}}{3}\hat{i}-\frac{1}{2}\hat{k}$

Answer

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

Answer

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

Answer

$\frac{\sqrt{2}}{3}\hat{i}-\frac{1}{2}\hat{k}$

Answer

$\frac{\sqrt{2}}{3}\hat{i}+\frac{1}{3\sqrt{2}}\hat{j}-\frac{1}{2}\hat{k}$

JEE Main 4 April 2024, Shift 1, Maths Q18

Same idea in other shifts