The cosine of the angle included between the | vedclass

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

Question

(B) The direction vectors of the two lines are $\vec{b_1} = \hat{\imath} - 2\hat{\jmath} - 2\hat{k}$ and $\vec{b_2} = 3\hat{\imath} + 2\hat{\jmath} -

Vedclass · Accepted Answer

$\frac{11}{21}$

Vedclass · Answer

(B) The direction vectors of the two lines are $\vec{b_1} = \hat{\imath} - 2\hat{\jmath} - 2\hat{k}$ and $\vec{b_2} = 3\hat{\imath} + 2\hat{\jmath} - 6\hat{k}$.The cosine of the angle $	heta$ between the lines is given by $\cos 	heta = \frac{|\vec{b_1} \cdot \vec{b_2}|}{|\vec{b_1}| |\vec{b_2}|}$.First,calculate the dot product: $\vec{b_1} \cdot \vec{b_2} = (1)(3) + (-2)(2) + (-2)(-6) = 3 - 4 + 12 = 11$.Next,calculate the magnitudes: $|\vec{b_1}| = \sqrt{1^2 + (-2)^2 + (-2)^2} = \sqrt{1 + 4 + 4} = \sqrt{9} = 3$.$|\vec{b_2}| = \sqrt{3^2 + 2^2 + (-6)^2} = \sqrt{9 + 4 + 36} = \sqrt{49} = 7$.Therefore,$\cos 	heta = \frac{|11|}{3 	imes 7} = \frac{11}{21}$.

The cosine of the angle included between the lines $\overline{r}=(2 \hat{\imath}+\hat{\jmath}-2 \hat{k})+\lambda(\hat{\imath}-2 \hat{\jmath}-2 \hat{k})$ and $\overline{r}=(\hat{\imath}+\hat{\jmath}+3 \hat{k})+\mu(3 \hat{\imath}+2 \hat{\jmath}-6 \hat{k})$ where $\lambda, \mu \in R$ is

Similar Questions

$P, Q, R$ and $S$ are four points with the position vectors $3i-4j+5k, 0i+0j+4k, -4i+5j+1k$ and $-3i+4j+3k$,respectively. Then,the line $PQ$ meets the line $RS$ at the point

The line joining points $(3, 5, -7)$ and $(-2, 1, 8)$ meets the $yz$-plane at which point?

The distance of the point $P(7, 10, 11)$ from the line $\frac{x-4}{1} = \frac{y-4}{0} = \frac{z-2}{3}$ along the line $\frac{x-9}{2} = \frac{y-13}{3} = \frac{z-17}{6}$ is

The shortest distance between the lines $\frac{x-4}{1} = \frac{y-3}{2} = \frac{z-2}{-3}$ and $\frac{x+2}{2} = \frac{y-6}{4} = \frac{z-5}{-5}$ is:

Let the line passing through the points $(-1,2,1)$ and parallel to the line $\frac{x-1}{2}=\frac{y+1}{3}=\frac{z}{4}$ intersect the line $\frac{x+2}{3}=\frac{y-3}{2}=\frac{z-4}{1}$ at the point $P$. Then the distance of $P$ from the point $Q(4,-5,1)$ is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module