If a line makes angles frac{pi}{3} and frac{p | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) Let the angles made by the line with the positive $x$,$y$,and $z$-axes be $\alpha$,$\beta$,and $\gamma$ respectively.Given $\alpha = \frac{\pi}{3}

Vedclass · Accepted Answer

$\frac{\pi}{3}$

Vedclass · Answer

(D) Let the angles made by the line with the positive $x$,$y$,and $z$-axes be $\alpha$,$\beta$,and $\gamma$ respectively.Given $\alpha = \frac{\pi}{3}$ and $\beta = \frac{\pi}{4}$.The direction cosines of the line are $l = \cos \alpha$,$m = \cos \beta$,and $n = \cos \gamma$.We know that $l^2 + m^2 + n^2 = 1$,which implies $\cos^2 \alpha + \cos^2 \beta + \cos^2 \gamma = 1$.Substituting the values: $\cos^2(\frac{\pi}{3}) + \cos^2(\frac{\pi}{4}) + \cos^2 \gamma = 1$.$(\frac{1}{2})^2 + (\frac{1}{\sqrt{2}})^2 + \cos^2 \gamma = 1$.$\frac{1}{4} + \frac{1}{2} + \cos^2 \gamma = 1$.$\frac{3}{4} + \cos^2 \gamma = 1$.$\cos^2 \gamma = 1 - \frac{3}{4} = \frac{1}{4}$.$\cos \gamma = \frac{1}{2}$ (since the angle is with the positive axis,$\cos \gamma > 0$).Therefore,$\gamma = \frac{\pi}{3}$.

If a line makes angles $\frac{\pi}{3}$ and $\frac{\pi}{4}$ with the positive $x$ and $y$-axes respectively,then the angle made by the line with the positive $z$-axis is

Similar Questions

If a line makes an angle of $45^\circ$ with the positive directions of each of $x$-axis and $y$-axis,then the angle that the line makes with the positive direction of the $z$-axis is .............. $^\circ$.

If $OA$ is equally inclined to $OX, OY$ and $OZ$ and if $A$ is $\sqrt{3}$ units from the origin, then $A$ is:

Find the direction cosines of $x$,$y$,and $z$-axis.

If the direction ratios of a line are $1, -3, 2$,what are its direction cosines?

The direction cosines of the line making angles $\frac{\pi}{4}, \frac{\pi}{3}$ and $\theta$ $(0 < \theta < \frac{\pi}{2})$ respectively with $X, Y$ and $Z$ axes are:

Vedclass Test Series

Exam Paper Generator

Online Exam Module