If 1, 2, 3 and -1, 0, 1 are the direction rat | vedclass

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

Question

(C) The direction ratios of the normal to the plane $AOB$ are given by the cross product of the vectors representing the rays $OA$ and $OB$. Let $\vec

Vedclass · Accepted Answer

$\frac{-1}{\sqrt{6}}, \frac{2}{\sqrt{6}}, \frac{-1}{\sqrt{6}}$

Vedclass · Answer

(C) The direction ratios of the normal to the plane $AOB$ are given by the cross product of the vectors representing the rays $OA$ and $OB$. Let $\vec{a} = \langle 1, 2, 3 angle$ and $\vec{b} = \langle -1, 0, 1 angle$. The normal vector $\vec{n}$ is given by $\vec{a} 	imes \vec{b}$.$\vec{n} = \begin{vmatrix} \hat{i} & \hat{j} & \hat{k} \ 1 & 2 & 3 \ -1 & 0 & 1 \end{vmatrix} = \hat{i}(2-0) - \hat{j}(1+3) + \hat{k}(0+2) = 2\hat{i} - 4\hat{j} + 2\hat{k}$.Thus, the direction ratios of the normal are $\langle 2, -4, 2 angle$, which can be simplified to $\langle 1, -2, 1 angle$ or $\langle -1, 2, -1 angle$.The magnitude of the vector $\langle -1, 2, -1 angle$ is $\sqrt{(-1)^2 + 2^2 + (-1)^2} = \sqrt{1 + 4 + 1} = \sqrt{6}$.The direction cosines are $\frac{-1}{\sqrt{6}}, \frac{2}{\sqrt{6}}, \frac{-1}{\sqrt{6}}$.

If $1, 2, 3$ and $-1, 0, 1$ are the direction ratios of the rays $OA$ and $OB$ respectively, then the direction cosines of a normal to the plane $AOB$ are

Similar Questions

The magnitude of the projection of the vector $2\hat{i}+\hat{j}+\hat{k}$ on the vector perpendicular to the plane containing the vectors $\hat{i}+\hat{j}+\hat{k}$ and $\hat{i}+2\hat{j}+3\hat{k}$ is:

If $\vec{a}, \vec{b}, \vec{c}$ are unit vectors such that $\vec{a} \cdot \vec{b} = \vec{a} \cdot \vec{c} = 0$ and the angle between $\vec{b}$ and $\vec{c}$ is $\pi / 3$,then $\vec{a}$ is equal to

If $A(3,2,-1), B(-2,2,-3)$ and $D(-2,5,-4)$ are the vertices of a parallelogram,then the area of the parallelogram is

$A$ unit vector perpendicular to the vectors $4i - j + 3k$ and $-2i + j - 2k$ is

$A$ unit vector which is perpendicular to the vector $2\hat{i} - \hat{j} + 2\hat{k}$ and is coplanar with the vectors $\hat{i} + \hat{j} - \hat{k}$ and $2\hat{i} + 2\hat{j} - \hat{k}$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module