The angle between the lines frac{x-2}{2} = fr | vedclass

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

Question

(D) The direction ratios of the first line are $\vec{a_1} = (2, -2, 1)$.The direction ratios of the second line are $\vec{a_2} = (1, 2, 2)$.The angle

Vedclass · Accepted Answer

$90$

Vedclass · Answer

(D) The direction ratios of the first line are $\vec{a_1} = (2, -2, 1)$.The direction ratios of the second line are $\vec{a_2} = (1, 2, 2)$.The angle $	heta$ between two lines with direction ratios $(a_1, b_1, c_1)$ and $(a_2, b_2, c_2)$ is given by $\cos 	heta = \frac{|a_1 a_2 + b_1 b_2 + c_1 c_2|}{\sqrt{a_1^2 + b_1^2 + c_1^2} \sqrt{a_2^2 + b_2^2 + c_2^2}}$.Substituting the values:$\cos 	heta = \frac{|(2)(1) + (-2)(2) + (1)(2)|}{\sqrt{2^2 + (-2)^2 + 1^2} \sqrt{1^2 + 2^2 + 2^2}}$$\cos 	heta = \frac{|2 - 4 + 2|}{\sqrt{4 + 4 + 1} \sqrt{1 + 4 + 4}}$$\cos 	heta = \frac{0}{\sqrt{9} \sqrt{9}} = 0$Since $\cos 	heta = 0$,we have $	heta = 90^{\circ}$.

The angle between the lines $\frac{x-2}{2} = \frac{y-3}{-2} = \frac{z-5}{1}$ and $\frac{x-2}{1} = \frac{y-3}{2} = \frac{z-5}{2}$ is $ . . . . . . $. (in $^{\circ}$)

Similar Questions

The angle between two lines $\frac{x + 1}{2} = \frac{y + 3}{2} = \frac{z - 4}{-1}$ and $\frac{x - 4}{1} = \frac{y + 4}{2} = \frac{z + 1}{2}$ is

If the line joining $(2,3,-1)$ and $(3,5,-3)$ is perpendicular to the line joining $A(1,2,3)$ and $B(\alpha, \beta, \gamma)$,then a possible point for $B$ is

If the direction ratios of a line are in the ratio $2 : 1 : 2$ and it intersects the lines $x = y + a = z$ and $x + a = 2y = 2z$,then the coordinates of the points of intersection are:

The shortest distance between the lines $\frac{x - 2}{3} = \frac{y - 4}{4} = \frac{z - 5}{5}$ and $\frac{x - 1}{2} = \frac{y - 2}{3} = \frac{z - 3}{4}$ is equal to -

If the lines $\frac{3-x}{2}=\frac{5y-2}{3\lambda+1}=5-z$ and $\frac{x+2}{-1}=\frac{1-3y}{7}=\frac{4-z}{2\mu}$ are at right angles,then $7\lambda-10\mu=$

Vedclass Test Series

Exam Paper Generator

Online Exam Module