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(D) The three vectors along the coordinate axes representing the adjacent sides of a cube of length $b$ are $b\hat{i}$,$b\hat{j}$,and $b\hat{k}$.The d

Vedclass · Accepted Answer

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

Vedclass · Answer

(D) The three vectors along the coordinate axes representing the adjacent sides of a cube of length $b$ are $b\hat{i}$,$b\hat{j}$,and $b\hat{k}$.The diagonal vector $\vec{A}$ passing through the origin is the resultant of these three vectors: $\vec{A} = b\hat{i} + b\hat{j} + b\hat{k}$.The magnitude of this diagonal vector is $|\vec{A}| = \sqrt{b^2 + b^2 + b^2} = \sqrt{3b^2} = b\sqrt{3}$.The unit vector $\hat{A}$ along the diagonal is given by $\hat{A} = \frac{\vec{A}}{|\vec{A}|} = \frac{b\hat{i} + b\hat{j} + b\hat{k}}{b\sqrt{3}} = \frac{\hat{i} + \hat{j} + \hat{k}}{\sqrt{3}}$.

If three vectors along coordinate axes represent the adjacent sides of a cube of length $b$,then the unit vector along its diagonal passing through the origin will be

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