The angle between the lines frac{x-3}{1}=frac | 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 $\vec{b_1} = (1, 2, 2)$.The direction ratios of the second line are $\vec{b_2} = (3, 2, 6)$.The angle $

Vedclass · Accepted Answer

$\cos^{-1}\left(\frac{19}{21}\right)$

Vedclass · Answer

(D) The direction ratios of the first line are $\vec{b_1} = (1, 2, 2)$.The direction ratios of the second line are $\vec{b_2} = (3, 2, 6)$.The angle $	heta$ between two lines with direction vectors $\vec{b_1}$ and $\vec{b_2}$ is given by $\cos 	heta = \frac{|\vec{b_1} \cdot \vec{b_2}|}{|\vec{b_1}| |\vec{b_2}|}$.Calculating the dot product: $\vec{b_1} \cdot \vec{b_2} = (1)(3) + (2)(2) + (2)(6) = 3 + 4 + 12 = 19$.Calculating the magnitudes: $|\vec{b_1}| = \sqrt{1^2 + 2^2 + 2^2} = \sqrt{1 + 4 + 4} = \sqrt{9} = 3$.$|\vec{b_2}| = \sqrt{3^2 + 2^2 + 6^2} = \sqrt{9 + 4 + 36} = \sqrt{49} = 7$.Thus,$\cos 	heta = \frac{19}{3 	imes 7} = \frac{19}{21}$.Therefore,$	heta = \cos^{-1}\left(\frac{19}{21}ight)$.

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

Similar Questions

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

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

The coordinates of the points on the line $\frac{x+2}{1}=\frac{y-1}{2}=\frac{z+1}{-2}$ at a distance of $12 \text{ units}$ from the point $A(-2, 1, -1)$ are

Let $(\alpha, \beta, \gamma)$ be the image of the point $A(8, 5, 7)$ in the line $\frac{x-1}{2} = \frac{y+1}{3} = \frac{z-2}{5}$. Then $\alpha + \beta + \gamma$ is equal to

The vector equation of the line whose Cartesian equations are $y=2$ and $4x-3z+5=0$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module