The angle between the pair of lines frac{x+3} | 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 $\vec{b_1} = \langle 3, 5, 4 \rangle$. The direction ratios of the second line are $\vec{b_2} = \langle

Vedclass · Accepted Answer

None of these

Vedclass · Answer

(D) The direction ratios of the first line are $\vec{b_1} = \langle 3, 5, 4 angle$. The direction ratios of the second line are $\vec{b_2} = \langle 1, 4, 2 angle$. The angle $	heta$ between two lines with direction ratios $\langle a_1, b_1, c_1 angle$ and $\langle a_2, b_2, c_2 angle$ is given by $\cos 	heta = \left| \frac{a_1 a_2 + b_1 b_2 + c_1 c_2}{\sqrt{a_1^2 + b_1^2 + c_1^2} \sqrt{a_2^2 + b_2^2 + c_2^2}} ight|$. Substituting the values: $\cos 	heta = \left| \frac{(3)(1) + (5)(4) + (4)(2)}{\sqrt{3^2 + 5^2 + 4^2} \sqrt{1^2 + 4^2 + 2^2}} ight|$ $\cos 	heta = \left| \frac{3 + 20 + 8}{\sqrt{9 + 25 + 16} \sqrt{1 + 16 + 4}} ight|$ $\cos 	heta = \left| \frac{31}{\sqrt{50} \sqrt{21}} ight| = \frac{31}{5 \sqrt{2} \sqrt{21}} = \frac{31}{5 \sqrt{42}}$. Thus,$	heta = \cos^{-1} \left( \frac{31}{5 \sqrt{42}} ight)$. Since this value is not present in the given options,the correct choice is $D$.

The angle between the pair of lines $\frac{x+3}{3}=\frac{y-1}{5}=\frac{z+3}{4}$ and $\frac{x+1}{1}=\frac{y-4}{4}=\frac{z-5}{2}$ is

Similar Questions

If the lines $\frac{x-k}{2}=\frac{y+1}{3}=\frac{z-1}{4}$ and $\frac{x-3}{1}=\frac{y-\frac{9}{2}}{2}=\frac{z}{1}$ intersect,then the value of $k$ is

If $2x - y + z = 0 = y - x + 2z = mx - 2y + mz$ represents a line in space,then the value of $m$ is-

If the lines $\frac{1-x}{2}=\frac{y-8}{\lambda}=\frac{z-5}{2}$ and $\frac{x-11}{5}=\frac{y-3}{3}=\frac{z-1}{1}$ are perpendicular,then $\lambda=$

The point collinear with $(1, -2, -3)$ and $(2, 0, 0)$ among the following is

The Cartesian equation of the line passing through the point $(5, -2, 4)$ and parallel to the vector $3\hat{i}-2\hat{j}+8\hat{k}$ is . . . . . . .

Vedclass Test Series

Exam Paper Generator

Online Exam Module