The cosine values of the angles made by the v | vedclass

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(A) Given vector $\vec{A} = \hat{i} + \hat{j} + \hat{k}$.Comparing with $\vec{A} = A_x\hat{i} + A_y\hat{j} + A_z\hat{k}$,we get $A_x = 1, A_y = 1, A_z

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$\frac{1}{\sqrt{3}}, \frac{1}{\sqrt{3}}, \frac{1}{\sqrt{3}}$

Vedclass · Answer

(A) Given vector $\vec{A} = \hat{i} + \hat{j} + \hat{k}$.Comparing with $\vec{A} = A_x\hat{i} + A_y\hat{j} + A_z\hat{k}$,we get $A_x = 1, A_y = 1, A_z = 1$.The magnitude of the vector is $|\vec{A}| = \sqrt{A_x^2 + A_y^2 + A_z^2} = \sqrt{1^2 + 1^2 + 1^2} = \sqrt{3}$.The direction cosines are given by $\cos \alpha = \frac{A_x}{|\vec{A}|} = \frac{1}{\sqrt{3}}$,$\cos \beta = \frac{A_y}{|\vec{A}|} = \frac{1}{\sqrt{3}}$,and $\cos \gamma = \frac{A_z}{|\vec{A}|} = \frac{1}{\sqrt{3}}$.Thus,the cosine values are $\frac{1}{\sqrt{3}}, \frac{1}{\sqrt{3}}, \frac{1}{\sqrt{3}}$.

The cosine values of the angles made by the vector $\vec{A} = \hat{i} + \hat{j} + \hat{k}$ with the $X$,$Y$,and $Z$ axes respectively are:

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