The direction cosine of the vector vec{a} = 3 | vedclass

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(C) The vector is given by $\vec{a} = 3\hat{i} + 4\hat{j} + 5\hat{k}$.To find the direction cosines,we first calculate the magnitude of the vector $\v

Vedclass · Accepted Answer

$\frac{3}{\sqrt{50}}$

Vedclass · Answer

(C) The vector is given by $\vec{a} = 3\hat{i} + 4\hat{j} + 5\hat{k}$.To find the direction cosines,we first calculate the magnitude of the vector $\vec{a}$:$|\vec{a}| = \sqrt{3^2 + 4^2 + 5^2} = \sqrt{9 + 16 + 25} = \sqrt{50}$.The direction cosine in the direction of the positive $x$-axis is given by the ratio of the $x$-component to the magnitude of the vector:$\cos \alpha = \frac{a_x}{|\vec{a}|} = \frac{3}{\sqrt{50}}$.Thus,the correct option is $C$.

The direction cosine of the vector $\vec{a} = 3\hat{i} + 4\hat{j} + 5\hat{k}$ in the direction of the positive $x$-axis is:

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