JEE Main 20244 Apr, Morning shiftMathematicsMediumVector Algebra184× since 2002Let a unit vector which makes an angle of 60∘60^{\circ}60∘ with 2i^+2j^−k^2 \hat{i}+2 \hat{j}-\hat{k}2i^+2j^−k^ and an angle of 45∘45^{\circ}45∘ with i^−k^\hat{i}-\hat{k}i^−k^ be C⃗\vec{C}C. Then C⃗+(−12i^+132j^−23k^)\vec{C}+\left(-\frac{1}{2} \hat{i}+\frac{1}{3 \sqrt{2}} \hat{j}-\frac{\sqrt{2}}{3} \hat{k}\right)C+(−21i^+321j^−32k^) is:AOption A. −23i^+23j^+(12+223)k^-\frac{\sqrt{2}}{3} \hat{i}+\frac{\sqrt{2}}{3} \hat{j}+\left(\frac{1}{2}+\frac{2 \sqrt{2}}{3}\right) \hat{k}−32i^+32j^+(21+322)k^BOption B. (13+12)i^+(13−132)j^+(13+23)k^\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}(31+21)i^+(31−321)j^+(31+32)k^COption C. 23i^−12k^\frac{\sqrt{2}}{3} \hat{i}-\frac{1}{2} \hat{k}32i^−21k^DOption D. 23i^+132j^−12k^\frac{\sqrt{2}}{3} \hat{i}+\frac{1}{3 \sqrt{2}} \hat{j}-\frac{1}{2} \hat{k}32i^+321j^−21k^CheckSkip · show solution
