The direction cosines of the line making angl | vedclass

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

Question

(A) Let the direction cosines be $l, m, n$. Given the angles $\alpha = \frac{\pi}{4}$, $\beta = \frac{\pi}{3}$, and $\gamma = 	heta$.Then $l = \cos \

Vedclass · Accepted Answer

$\frac{1}{\sqrt{2}}, \frac{1}{2}, \frac{1}{2}$

Vedclass · Answer

(A) Let the direction cosines be $l, m, n$. Given the angles $\alpha = \frac{\pi}{4}$, $\beta = \frac{\pi}{3}$, and $\gamma = 	heta$.Then $l = \cos \frac{\pi}{4} = \frac{1}{\sqrt{2}}$ and $m = \cos \frac{\pi}{3} = \frac{1}{2}$.We know that $l^2 + m^2 + n^2 = 1$.Substituting the values, we get $\left(\frac{1}{\sqrt{2}}ight)^2 + \left(\frac{1}{2}ight)^2 + \cos^2 	heta = 1$.$\frac{1}{2} + \frac{1}{4} + \cos^2 	heta = 1$.$\frac{3}{4} + \cos^2 	heta = 1$.$\cos^2 	heta = 1 - \frac{3}{4} = \frac{1}{4}$.Since $0 Thus, the direction cosines are $\frac{1}{\sqrt{2}}, \frac{1}{2}, \frac{1}{2}$.

The direction cosines of the line making angles $\frac{\pi}{4}, \frac{\pi}{3}$ and $\theta$ $\left(0 < \theta < \frac{\pi}{2}\right)$ respectively with $x, y$ and $z$ axes, are

Similar Questions

Ecdysone is produced by

If $\cos A = \frac{3}{4}$,then $32 \sin \left(\frac{A}{2}\right) \sin \left(\frac{5A}{2}\right) = $

If a polygon of $n$ sides has $275$ diagonals,then $n$ is equal to

An ammeter gives full scale deflection when a current of $1.0 \ A$ is passed through it. To convert it into a $10 \ A$ range ammeter,the ratio of its resistance $(G)$ to the shunt resistance $(S)$ will be:

$\cos 36^{\circ} - \cos 72^{\circ}$ is equal to

Vedclass Test Series

Exam Paper Generator

Online Exam Module