If a line makes angles alpha, beta, gamma wit | vedclass

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

Question

(B) We know that for a line with direction angles $\alpha, \beta, \gamma$,the direction cosines are $\cos \alpha, \cos \beta, \cos \gamma$. According

Vedclass · Accepted Answer

$-1$

Vedclass · Answer

(B) We know that for a line with direction angles $\alpha, \beta, \gamma$,the direction cosines are $\cos \alpha, \cos \beta, \cos \gamma$. According to the property of direction cosines,$\cos^2 \alpha + \cos^2 \beta + \cos^2 \gamma = 1$. We need to evaluate $\cos 2\alpha + \cos 2\beta + \cos 2\gamma$. Using the identity $\cos 2	heta = 2\cos^2 	heta - 1$,we get: $\cos 2\alpha + \cos 2\beta + \cos 2\gamma = (2\cos^2 \alpha - 1) + (2\cos^2 \beta - 1) + (2\cos^2 \gamma - 1)$ $= 2(\cos^2 \alpha + \cos^2 \beta + \cos^2 \gamma) - 3$ $= 2(1) - 3 = 2 - 3 = -1$.

If a line makes angles $\alpha, \beta, \gamma$ with the three-dimensional coordinate axes respectively,then $\cos 2\alpha + \cos 2\beta + \cos 2\gamma = $

Similar Questions

The angle between the straight lines,whose direction cosines are given by the equations $2l + 2m - n = 0$ and $mn + nl + lm = 0$,is:

If the direction ratios $a, b, c$ of a line $L$ satisfy the relations $ab + bc + ca = 0$ and $6ab + 9bc + 8ca = 0$, then the direction cosines of the line $L$ are

If the projections of a line on the coordinate axes are $2, -1, 2$,then the length of the line is

The angle between the lines whose direction ratios satisfy the equations $l+m+n=0$ and $l^2=m^2+n^2$ is

The projection of the line segment joining $P(2, -1, 0)$ and $Q(3, 2, -1)$ on the line whose direction ratios are $1, 2, 2$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module