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If $\hat{i}$ , $\hat{j}$ and $\hat{k}$ are unit vectors along x, y and z-axes respectively, the angle $θ$ between the vector $\hat{i} + \hat{j} + \hat{k}$ and vector $\hat{i}$ is given by

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θ=cos−1(13)

θ=sin−1(13)

θ=cos−1(32)

θ=sin−1(32)

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detailed solution

Correct option is A

cosθ=(i^+j^+k^). i^(12+12+12)12×12=i^.i^+j^.i^+k.i^(1+1+1)12×1=1+0+03=13

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If i^ , j^ and k^ are unit vectors along x, y and z-axes respectively, the angle θ between the vector i^+j^+k^ and vector i^ is given by

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If $\hat{i}$ , $\hat{j}$ and $\hat{k}$ are unit vectors along x, y and z-axes respectively, the angle $θ$ between the vector $\hat{i} + \hat{j} + \hat{k}$ and vector $\hat{i}$ is given by