Find the direction cosines of the line passin | vedclass

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

Question

(C) The direction ratios of the line passing through $P(x_{1}, y_{1}, z_{1})$ and $Q(x_{2}, y_{2}, z_{2})$ are given by $(x_{2}-x_{1}, y_{2}-y_{1}, z_

Vedclass · Accepted Answer

Both $A$ and $B$

Vedclass · Answer

(C) The direction ratios of the line passing through $P(x_{1}, y_{1}, z_{1})$ and $Q(x_{2}, y_{2}, z_{2})$ are given by $(x_{2}-x_{1}, y_{2}-y_{1}, z_{2}-z_{1})$.For points $P(2, 3, 5)$ and $Q(-1, 2, 4)$,the direction ratios are $(-1-2, 2-3, 4-5) = (-3, -1, -1)$.The distance $PQ$ is $\sqrt{(-3)^{2} + (-1)^{2} + (-1)^{2}} = \sqrt{9 + 1 + 1} = \sqrt{11}$.The direction cosines are obtained by dividing the direction ratios by the distance $PQ$.Thus,the direction cosines are $\left(\frac{-3}{\sqrt{11}}, \frac{-1}{\sqrt{11}}, \frac{-1}{\sqrt{11}}\right)$ or $\left(\frac{3}{\sqrt{11}}, \frac{1}{\sqrt{11}}, \frac{1}{\sqrt{11}}\right)$.

Find the direction cosines of the line passing through the points $P(2, 3, 5)$ and $Q(-1, 2, 4)$.

Similar Questions

If $(l_1, m_1, n_1)$ and $(l_2, m_2, n_2)$ are the direction cosines of two lines satisfying the relations $l^2+mn-6n^2=0$ and $2l-m+3n=0$,then $|l_1 l_2|+|m_1 m_2|=$

Find the octants in which the points $(-3, 1, 2)$ and $(-3, 1, -2)$ lie.

If a line makes angles of measure $\frac{\pi}{6}$ and $\frac{\pi}{3}$ with $X$ and $Y$ axes respectively,then the angle made by the line with $Z$ axis is

If the direction ratios of a line are $1, -3, 2$,what are its direction cosines?

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

Vedclass Test Series

Exam Paper Generator

Online Exam Module