If a line makes angles 90^{circ},135^{circ},a | vedclass

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Question

(A) The direction cosines of a line making angles $\alpha, \beta, \gamma$ with the $X, Y, Z$-axes are given by $\cos \alpha, \cos \beta, \cos \gamma$.

Vedclass · Accepted Answer

$\left(0, -\frac{1}{\sqrt{2}}, \frac{1}{\sqrt{2}}\right)$

Vedclass · Answer

(A) The direction cosines of a line making angles $\alpha, \beta, \gamma$ with the $X, Y, Z$-axes are given by $\cos \alpha, \cos \beta, \cos \gamma$. Given $\alpha = 90^{\circ}$,$\beta = 135^{\circ}$,and $\gamma = 45^{\circ}$. Calculating the values: $\cos \alpha = \cos 90^{\circ} = 0$ $\cos \beta = \cos 135^{\circ} = \cos(180^{\circ} - 45^{\circ}) = -\cos 45^{\circ} = -\frac{1}{\sqrt{2}}$ $\cos \gamma = \cos 45^{\circ} = \frac{1}{\sqrt{2}}$ Thus,the direction cosines are $\left(0, -\frac{1}{\sqrt{2}}, \frac{1}{\sqrt{2}}\right)$.

If a line makes angles $90^{\circ}$,$135^{\circ}$,and $45^{\circ}$ with the positive directions of $X$,$Y$,and $Z$-axes respectively,then its direction cosines are:

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