If the lengths of projections of a line of le | 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 $(l, m, n)$. Since the length of the line is $l$,the projections of the line on the coordinate axes are g

Vedclass · Accepted Answer

$l^2$

Vedclass · Answer

(C) Let the direction cosines of the line be $(l, m, n)$. Since the length of the line is $l$,the projections of the line on the coordinate axes are given by $l_1 = l \cdot |l|$,$l_2 = l \cdot |m|$,and $l_3 = l \cdot |n|$.Squaring these,we get $l_1^2 = l^2 l^2$,$l_2^2 = l^2 m^2$,and $l_3^2 = l^2 n^2$.Adding these equations,we get $l_1^2 + l_2^2 + l_3^2 = l^2 (l^2 + m^2 + n^2)$.Since the sum of the squares of the direction cosines is $l^2 + m^2 + n^2 = 1$,we have $l_1^2 + l_2^2 + l_3^2 = l^2 (1) = l^2$.

If the lengths of projections of a line of length $l$ over the coordinate axes are $l_1, l_2$ and $l_3$ respectively,then $l_1^2+l_2^2+l_3^2$ is equal to

Similar Questions

If the direction cosines of two lines are given by $l+m+n=0$ and $l^2-5m^2+n^2=0$, then the angle between them is

If $\alpha, \beta$ and $\gamma$ are the angles which a half ray makes with the positive direction of the axes,then $\sin ^{2} \alpha+\sin ^{2} \beta+\sin ^{2} \gamma$ is equal to

The angle between the lines whose direction ratios satisfy the equations $l+m+n=0$ and $l^2=m^2+n^2$ is

The direction cosines $\ell, m, n$ of the line $\frac{x+2}{2}=\frac{2y-4}{3}; z=-1$ are:

$A$ vector $\overline{OP}$ makes angles of $45^{\circ}$ with $OX$ and $60^{\circ}$ with $OY$. Find the angle that $\overline{OP}$ makes with $OZ$ (in degrees).

Vedclass Test Series

Exam Paper Generator

Online Exam Module