The angle between the straight lines frac{x + | 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 $a_1 = 2, b_1 = 5, c_1 = 4$.The direction ratios of the second line are $a_2 = 1, b_2 = 2, c_2 = -3$.Le

Vedclass · Accepted Answer

$90$

Vedclass · Answer

(D) The direction ratios of the first line are $a_1 = 2, b_1 = 5, c_1 = 4$.The direction ratios of the second line are $a_2 = 1, b_2 = 2, c_2 = -3$.Let $	heta$ be the angle between the lines. The formula for the angle is $\cos 	heta = \frac{|a_1 a_2 + b_1 b_2 + c_1 c_2|}{\sqrt{a_1^2 + b_1^2 + c_1^2} \sqrt{a_2^2 + b_2^2 + c_2^2}}$.Substituting the values: $\cos 	heta = \frac{|(2)(1) + (5)(2) + (4)(-3)|}{\sqrt{2^2 + 5^2 + 4^2} \sqrt{1^2 + 2^2 + (-3)^2}}$.$\cos 	heta = \frac{|2 + 10 - 12|}{\sqrt{4 + 25 + 16} \sqrt{1 + 4 + 9}} = \frac{|0|}{\sqrt{45} \sqrt{14}} = 0$.Since $\cos 	heta = 0$,we have $	heta = 90^o$.

The angle between the straight lines $\frac{x + 1}{2} = \frac{y - 2}{5} = \frac{z + 3}{4}$ and $\frac{x - 1}{1} = \frac{y + 2}{2} = \frac{z - 3}{-3}$ is ......... $^o$

Similar Questions

The angle between the lines $\frac{x}{2}=\frac{y}{2}=\frac{z}{1}$ and $\frac{x-5}{4}=\frac{y-2}{1}=\frac{z-3}{8}$ is . . . . . . .

If the foot of the perpendicular drawn from the point $A(1, 0, 3)$ on a line passing through $B(\alpha, 7, 1)$ is $P\left(\frac{5}{3}, \frac{7}{3}, \frac{17}{3}\right)$,then $\alpha$ is equal to:

If $\vec{r}=\hat{i}+\hat{j}+t(2 \hat{i}-\hat{j}+\hat{k})$ and $\vec{r}=2 \hat{i}-\hat{j}-\hat{k}+s(3 \hat{i}-5 \hat{j}+2 \hat{k})$ are the vector equations of two lines $L_1$ and $L_2$,then the shortest distance between them is

The direction cosines of two lines are connected by the relations $l+m-n=0$ and $lm-2mn+nl=0$. If $\theta$ is the acute angle between those lines,then $\cos \theta=$

The square of the distance of the point $\left(\frac{15}{7}, \frac{32}{7}, 7\right)$ from the line $\frac{x+1}{3}=\frac{y+3}{5}=\frac{z+5}{7}$ in the direction of the vector $\hat{i}+4 \hat{j}+7 \hat{k}$ is :

Vedclass Test Series

Exam Paper Generator

Online Exam Module