Find the direction cosines of a line which ma | vedclass

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

Question

(A) Let the direction cosines of the line be $l, m, n$. Since the line makes equal angles $\alpha$ with the coordinate axes,we have $l = \cos \alpha$,

Vedclass · Accepted Answer

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

Vedclass · Answer

(A) Let the direction cosines of the line be $l, m, n$. Since the line makes equal angles $\alpha$ with the coordinate axes,we have $l = \cos \alpha$,$m = \cos \alpha$,and $n = \cos \alpha$.We know that $l^2 + m^2 + n^2 = 1$.Substituting the values,we get $\cos^2 \alpha + \cos^2 \alpha + \cos^2 \alpha = 1$.This simplifies to $3 \cos^2 \alpha = 1$,which implies $\cos^2 \alpha = \frac{1}{3}$.Therefore,$\cos \alpha = \pm \frac{1}{\sqrt{3}}$.Thus,the direction cosines are $\pm \frac{1}{\sqrt{3}}, \pm \frac{1}{\sqrt{3}}, \pm \frac{1}{\sqrt{3}}$.

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

Similar Questions

If $\ell, m, n$ and $a, b, c$ are direction cosines of two lines,then:

The direction cosines of a line segment $AB$ are $-2/\sqrt{17}, 3/\sqrt{17}, -2/\sqrt{17}$. If $AB = \sqrt{17}$ and the coordinates of $A$ are $(3, -6, 10)$,then the coordinates of $B$ are

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

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 direction cosines of two lines are such that $2l + m + 2n = 0$ and $3l^2 + 5m^2 - 11n^2 = 0$,then the angle between the two lines is

Vedclass Test Series

Exam Paper Generator

Online Exam Module