The direction cosines of a line which is perp | vedclass

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

Question

(B) Let $\vec{a} = 3\hat{i} - 2\hat{j} + 4\hat{k}$ and $\vec{b} = 1\hat{i} + 3\hat{j} - 2\hat{k}$.Since the line is perpendicular to both lines,its di

Vedclass · Accepted Answer

$\frac{-8}{\sqrt{285}}, \frac{10}{\sqrt{285}}, \frac{11}{\sqrt{285}}$

Vedclass · Answer

(B) Let $\vec{a} = 3\hat{i} - 2\hat{j} + 4\hat{k}$ and $\vec{b} = 1\hat{i} + 3\hat{j} - 2\hat{k}$.Since the line is perpendicular to both lines,its direction vector is given by the cross product $\vec{n} = \vec{a} 	imes \vec{b}$.$\vec{n} = \begin{vmatrix} \hat{i} & \hat{j} & \hat{k} \ 3 & -2 & 4 \ 1 & 3 & -2 \end{vmatrix} = \hat{i}(4 - 12) - \hat{j}(-6 - 4) + \hat{k}(9 + 2) = -8\hat{i} + 10\hat{j} + 11\hat{k}$.The magnitude of the vector is $|\vec{n}| = \sqrt{(-8)^2 + 10^2 + 11^2} = \sqrt{64 + 100 + 121} = \sqrt{285}$.The direction cosines are the components of the unit vector,which are $\frac{-8}{\sqrt{285}}, \frac{10}{\sqrt{285}}, \frac{11}{\sqrt{285}}$.

The direction cosines of a line which is perpendicular to lines whose direction ratios are $3, -2, 4$ and $1, 3, -2$ are

Similar Questions

$A$ unit vector perpendicular to the vectors $\vec{a} = 2 \hat{i} + 3 \hat{j} + 4 \hat{k}$ and $\vec{b} = 3 \hat{j} + 2 \hat{k}$ is

The area of the parallelogram whose diagonals are represented by the vectors $\bar{a}=3 \hat{i}-\hat{j}-2 \hat{k}$ and $\bar{b}=-\hat{i}+3 \hat{j}-3 \hat{k}$ is

$A$ unit vector perpendicular to both the vectors $\hat{i}+\hat{j}$ and $\hat{j}+\hat{k}$ is

The position vectors of the points $A, B, C$ are $\hat{i}+2\hat{j}-\hat{k}, \hat{i}+\hat{j}+\hat{k}$,and $2\hat{i}+3\hat{j}+2\hat{k}$ respectively. If $A$ is chosen as the origin,then the cross product of the position vectors of $B$ and $C$ is:

If $a \times b = b \times c \ne 0$ and $a + c \ne 0,$ then

Vedclass Test Series

Exam Paper Generator

Online Exam Module