The direction cosines of the line joining the | vedclass

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

Question

(A) Let the points be $P(4, 3, -5)$ and $Q(-2, 1, -8)$.The direction ratios $(a, b, c)$ of the line segment $PQ$ are given by $(x_2 - x_1, y_2 - y_1,

Vedclass · Accepted Answer

$\left( \frac{6}{7}, \frac{2}{7}, \frac{3}{7} \right)$

Vedclass · Answer

(A) Let the points be $P(4, 3, -5)$ and $Q(-2, 1, -8)$.The direction ratios $(a, b, c)$ of the line segment $PQ$ are given by $(x_2 - x_1, y_2 - y_1, z_2 - z_1)$.$a = -2 - 4 = -6$$b = 1 - 3 = -2$$c = -8 - (-5) = -3$The distance $PQ = \sqrt{(-6)^2 + (-2)^2 + (-3)^2} = \sqrt{36 + 4 + 9} = \sqrt{49} = 7$.The direction cosines $(l, m, n)$ are given by $\left( \frac{a}{PQ}, \frac{b}{PQ}, \frac{c}{PQ} \right)$.$l = \frac{-6}{7}, m = \frac{-2}{7}, n = \frac{-3}{7}$.Alternatively,if we consider the direction from $Q$ to $P$,the direction cosines are $\left( \frac{6}{7}, \frac{2}{7}, \frac{3}{7} \right)$.Comparing with the given options,the correct option is $A$.

The direction cosines of the line joining the points $(4, 3, -5)$ and $(-2, 1, -8)$ are

Similar Questions

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

$ABC$ is a triangle in a plane with vertices $A(2, 3, 5)$,$B(-1, 3, 2)$,and $C(\lambda, 5, \mu)$. If the median through $A$ is equally inclined to the coordinate axes,then the value of $(\lambda^3 + \mu^3 + 5)$ is

If a line makes an angle of $\frac{\pi}{3}$ with each of the $X$ and $Y$-axes,then the acute angle made by the line with the $Z$-axis is:

The angle between a line with direction ratios $2, 2, 1$ and a line joining $(3, 1, 4)$ and $(7, 2, 12)$ is

If $(a_1, b_1, c_1)$ and $(a_2, b_2, c_2)$ are the direction cosines of two lines making an angle $\theta$ with each other,then $\cos \theta =$

Vedclass Test Series

Exam Paper Generator

Online Exam Module