A unit vector makes an angle with Z-axis

MATHEMATICS · Single correct · CBSE · Mathematics · Vector Algebra · Vector Algebra

Problem

A unit vector a\boldsymbol{a} makes an angle π4\frac{\pi}{4} with Z-axis. If a+i^+j^\boldsymbol{a} + \hat{\boldsymbol{i}} + \hat{\boldsymbol{j}} is a unit vector, then a\boldsymbol{a} is equal to (1) i^2+j^2+k^2\frac{\hat{\boldsymbol{i}}}{2} + \frac{\hat{\boldsymbol{j}}}{2} + \frac{\hat{\boldsymbol{k}}}{\sqrt{2}} (2) i^2+j^2−k^2\frac{\hat{\boldsymbol{i}}}{2} + \frac{\hat{\boldsymbol{j}}}{2} - \frac{\hat{\boldsymbol{k}}}{\sqrt{2}} (3) −i^2−j^2+k^2-\frac{\hat{\boldsymbol{i}}}{2} - \frac{\hat{\boldsymbol{j}}}{2} + \frac{\hat{\boldsymbol{k}}}{\sqrt{2}} (4) None of these

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