If the direction cosines of a line are left( | vedclass

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

Question

(B) The direction cosines of a line are given as $l = \frac{1}{c}$,$m = \frac{1}{c}$,and $n = \frac{1}{c}$.We know that for any line,the sum of the sq

Vedclass · Accepted Answer

$c = \pm \sqrt{3}$

Vedclass · Answer

(B) The direction cosines of a line are given as $l = \frac{1}{c}$,$m = \frac{1}{c}$,and $n = \frac{1}{c}$.We know that for any line,the sum of the squares of its direction cosines is always equal to $1$,i.e.,$l^2 + m^2 + n^2 = 1$.Substituting the given values,we get:$\left( \frac{1}{c} \right)^2 + \left( \frac{1}{c} \right)^2 + \left( \frac{1}{c} \right)^2 = 1$$\frac{1}{c^2} + \frac{1}{c^2} + \frac{1}{c^2} = 1$$\frac{3}{c^2} = 1$$c^2 = 3$$c = \pm \sqrt{3}$.

If the direction cosines of a line are $\left( \frac{1}{c}, \frac{1}{c}, \frac{1}{c} \right)$,then

Similar Questions

If the projections of a line segment on the coordinate axes are $3, 4,$ and $5$,then its length is:

Find the angle between two lines whose direction cosines are given by the relations $l + m + n = 0$ and $l^2 + m^2 - n^2 = 0$.

What are the direction cosines of a line perpendicular to the $yz$-plane?

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 ...

The direction cosines of the line passing through $P(2, 3, -1)$ and the origin are

Vedclass Test Series

Exam Paper Generator

Online Exam Module