If the projections of a line segment on the c | vedclass

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

Question

(A) Let the length of the line segment be $r$ and its direction cosines be $l, m, n$.The projections of the line segment on the coordinate axes are gi

Vedclass · Accepted Answer

$7$

Vedclass · Answer

(A) Let the length of the line segment be $r$ and its direction cosines be $l, m, n$.The projections of the line segment on the coordinate axes are given by $lr, mr, nr$.Given that $lr = 2, mr = 3$,and $nr = 6$.Squaring and adding these equations,we get:$(lr)^2 + (mr)^2 + (nr)^2 = 2^2 + 3^2 + 6^2$$r^2(l^2 + m^2 + n^2) = 4 + 9 + 36$Since the sum of the squares of the direction cosines is $l^2 + m^2 + n^2 = 1$,we have:$r^2(1) = 49$$r^2 = 49$$r = 7$Thus,the length of the line segment is $7$.

If the projections of a line segment on the coordinate axes are $2, 3, 6$,find the length of the line segment.

Similar Questions

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

If the angle between the lines whose direction ratios are $4, -3, 5$ and $3, 4, k$ is $\frac{\pi}{3}$,then $k=$

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

The direction cosines of the line passing through $P(2, 3, -1)$ and the origin are

Vedclass Test Series

Exam Paper Generator

Online Exam Module