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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} a makes an angle π 4 \frac{\pi}{4} 4 π with Z-axis. If
a + i ^ + j ^ \boldsymbol{a} + \hat{\boldsymbol{i}} + \hat{\boldsymbol{j}} a + i ^ + j ^ is a unit vector, then a \boldsymbol{a} 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) 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 ^
(3) − 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 ^
(4) None of these
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