If the direction cosines (l, m, n) of two lin | vedclass

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

Question

(A) Given the relations for the direction cosines $(l, m, n)$ of the two lines: $l+m+n=0$ and $lm=0$ From $lm=0$, we have two cases: $l=0$ or $m=0$. C

Vedclass · Accepted Answer

$\frac{\pi}{3}$

Vedclass · Answer

(A) Given the relations for the direction cosines $(l, m, n)$ of the two lines: $l+m+n=0$ and $lm=0$ From $lm=0$, we have two cases: $l=0$ or $m=0$. Case $1$: If $l=0$, then $0+m+n=0 \Rightarrow n=-m$. The direction ratios are $(0, m, -m)$, which simplifies to $(0, 1, -1)$. Case $2$: If $m=0$, then $l+0+n=0 \Rightarrow n=-l$. The direction ratios are $(l, 0, -l)$, which simplifies to $(1, 0, -1)$. Let the direction vectors be $\vec{a} = (0, 1, -1)$ and $\vec{b} = (1, 0, -1)$. The cosine of the angle $	heta$ between the two lines is given by: $\cos 	heta = \frac{|\vec{a} \cdot \vec{b}|}{|\vec{a}| |\vec{b}|} = \frac{|(0)(1) + (1)(0) + (-1)(-1)|}{\sqrt{0^2+1^2+(-1)^2} \cdot \sqrt{1^2+0^2+(-1)^2}}$ $\cos 	heta = \frac{|0 + 0 + 1|}{\sqrt{2} \cdot \sqrt{2}} = \frac{1}{2}$ Therefore, $	heta = \cos^{-1}(\frac{1}{2}) = \frac{\pi}{3}$.

If the direction cosines $(l, m, n)$ of two lines are connected by the relations $l+m+n=0$ and $lm=0$, then the angle between those lines is

Similar Questions

Let $\alpha$ be the angle between the lines whose direction cosines satisfy the equations $l+m-n=0$ and $l^{2}+m^{2}-n^{2}=0$. Then the value of $\sin^{4} \alpha + \cos^{4} \alpha$ is

What do the three lines with direction ratios $(1, 1, 2)$,$(\sqrt{3}-1, -\sqrt{3}-1, 4)$,and $(-\sqrt{3}-1, \sqrt{3}-1, 4)$ represent?

$A$ line makes angles $\alpha, \beta, \gamma$ with the coordinate axes and $\alpha+\beta=90^{\circ}$,then $\gamma=$ (in $^{\circ}$)

The length of the projection of the line segment joining the points $(3, 4, 5)$ and $(4, 6, 3)$ on the line joining the points $(-1, 2, 4)$ and $(1, 0, 5)$ 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