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

If a line lies in the octant $OXYZ$ and it makes equal angles with the axes,then

The angle between the lines whose direction cosines are $\left(\frac{\sqrt{3}}{4}, \frac{1}{4}, \frac{\sqrt{3}}{2}\right)$ and $\left(\frac{\sqrt{3}}{4}, \frac{1}{4}, \frac{-\sqrt{3}}{2}\right)$ is

The direction cosines of a line equally inclined to three mutually perpendicular lines having direction cosines as $(l_1, m_1, n_1)$,$(l_2, m_2, n_2)$ and $(l_3, m_3, n_3)$ are:

The octant in which the point $(2, -4, -7)$ lies is

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