If a line lies in the octant OXYZ and it make | vedclass

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

Question

(B) Let the direction cosines of the line be $l, m, n$. Since the line makes equal angles with the axes,we have $\alpha = \beta = \gamma$. Thus,$l = \

Vedclass · Accepted Answer

$l = m = n = \pm \frac{1}{\sqrt{3}}$

Vedclass · Answer

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

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

Similar Questions

The direction cosines of the line $\frac{3x + 1}{-3} = \frac{3y + 2}{6} = \frac{z}{-1}$ are

The direction cosines of three lines passing through the origin are $(l_1, m_1, n_1)$,$(l_2, m_2, n_2)$,and $(l_3, m_3, n_3)$. The lines will be coplanar if

If a line makes angles $\frac{\pi}{4}$ and $\frac{\pi}{3}$ with $Y$-axis and $Z$-axis respectively,then the obtuse angle made by that line with $X$-axis is

If the coordinates of $A$ and $B$ are $(1, 2, 3)$ and $(7, 8, 7)$,then the projections of the line segment $AB$ on the coordinate axes are:

The direction cosines of the line $x = y = z$ are

Vedclass Test Series

Exam Paper Generator

Online Exam Module