If alpha, beta, gamma are the direction angle | vedclass

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

Question

(A) The direction cosines of a vector satisfy the identity $\cos^2 \alpha + \cos^2 \beta + \cos^2 \gamma = 1$. Given $\cos \alpha = \frac{14}{15}$ and

Vedclass · Accepted Answer

$\pm \frac{2}{15}$

Vedclass · Answer

(A) The direction cosines of a vector satisfy the identity $\cos^2 \alpha + \cos^2 \beta + \cos^2 \gamma = 1$. Given $\cos \alpha = \frac{14}{15}$ and $\cos \beta = \frac{1}{3}$. Substituting these values into the identity: $\left( \frac{14}{15} \right)^2 + \left( \frac{1}{3} \right)^2 + \cos^2 \gamma = 1$ $\frac{196}{225} + \frac{1}{9} + \cos^2 \gamma = 1$ $\frac{196}{225} + \frac{25}{225} + \cos^2 \gamma = 1$ $\frac{221}{225} + \cos^2 \gamma = 1$ $\cos^2 \gamma = 1 - \frac{221}{225} = \frac{4}{225}$ $\cos \gamma = \pm \sqrt{\frac{4}{225}} = \pm \frac{2}{15}$.

If $\alpha, \beta, \gamma$ are the direction angles of a vector and $\cos \alpha = \frac{14}{15}$,$\cos \beta = \frac{1}{3}$,then $\cos \gamma = $

Similar Questions

If a line makes angles $\alpha, \beta, \gamma$ with the coordinate axes, then the sum of values of $\sin^2 \alpha + \sin^2 \beta + \sin^2 \gamma$ and $\cos 2\alpha + \cos 2\beta + \cos 2\gamma$ is ...

If a line makes angles $120^{\circ}$ and $60^{\circ}$ with the positive directions of $X$ and $Z$ axes respectively,then the angle made by the line with the positive $Y$-axis is (in $^{\circ}$)

The length of the projection of the line segment joining the points $(3, 4, 5)$ and $(4, 6, 3)$ on the line joining the points $(-1, 2, 4)$ and $(1, 0, 5)$ is

The acute angle between the two lines whose direction ratios $(l, m, n)$ satisfy the equations $l+m-n=0$ and $l^2+m^2-n^2=0$ is

If a line has the direction ratios $-18, 12, -4,$ then what are its direction cosines?

Vedclass Test Series

Exam Paper Generator

Online Exam Module