The direction cosines of a line which makes e | vedclass

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

Question

(C) Let the direction cosines of the line be $(l, m, n) = (\cos \alpha, \cos \beta, \cos \gamma)$.
We know that for any line,the sum of the squares o

Vedclass · Accepted Answer

$ < \frac{\pm 1}{\sqrt{3}}, \frac{\pm 1}{\sqrt{3}}, \frac{\pm 1}{\sqrt{3}}>$

Vedclass · Answer

(C) Let the direction cosines of the line be $(l, m, n) = (\cos \alpha, \cos \beta, \cos \gamma)$.
We know that for any line,the sum of the squares of its direction cosines is $l^2 + m^2 + n^2 = 1$.
Given that the line makes equal angles with the coordinate axes,we have $\alpha = \beta = \gamma$.
Therefore,$\cos \alpha = \cos \beta = \cos \gamma$.
Substituting this into the identity,we get $\cos^2 \alpha + \cos^2 \alpha + \cos^2 \alpha = 1$.
$3 \cos^2 \alpha = 1 \Rightarrow \cos^2 \alpha = \frac{1}{3}$.
Thus,$\cos \alpha = \pm \frac{1}{\sqrt{3}}$.
Hence,the direction cosines are $(\pm \frac{1}{\sqrt{3}}, \pm \frac{1}{\sqrt{3}}, \pm \frac{1}{\sqrt{3}})$.

The direction cosines of a line which makes equal angles with the coordinate axes are . . . . . .

Similar Questions

The direction cosines of the line $\frac{x-1}{0}=\frac{y+1}{5}=\frac{z-3}{0}$ are . . . . . . .

If the direction cosines $(l, m, n)$ of two lines are connected by the relations $l+m+n=0$ and $lm=0$,then the angle between those lines is

The direction cosines of the line,which is perpendicular to the lines with direction ratios $-1, 2, 2$ and $0, 2, 1$,are respectively

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

Find a vector $\vec{r}$ of magnitude $3 \sqrt{2}$ units which makes an angle of $\frac{\pi}{4}$ and $\frac{\pi}{2}$ with $y$ and $z$-axes,respectively.

Vedclass Test Series

Exam Paper Generator

Online Exam Module