The equation of the plane passing through the | vedclass

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

Question

(A) Let the normal vectors of the two given planes be $\vec{n_1} = 3\hat{i} + \hat{j} - 2\hat{k}$ and $\vec{n_2} = 2\hat{i} - 5\hat{j} - \hat{k}$.Sinc

Vedclass · Accepted Answer

$11x + y + 17z + 38 = 0$

Vedclass · Answer

(A) Let the normal vectors of the two given planes be $\vec{n_1} = 3\hat{i} + \hat{j} - 2\hat{k}$ and $\vec{n_2} = 2\hat{i} - 5\hat{j} - \hat{k}$.Since the required plane is perpendicular to both,its normal vector $\vec{n}$ is given by the cross product $\vec{n_1} 	imes \vec{n_2}$.$\vec{n} = \begin{vmatrix} \hat{i} & \hat{j} & \hat{k} \ 3 & 1 & -2 \ 2 & -5 & -1 \end{vmatrix} = \hat{i}(-1 - 10) - \hat{j}(-3 + 4) + \hat{k}(-15 - 2) = -11\hat{i} - \hat{j} - 17\hat{k}$.We can take the normal vector as $\vec{n} = 11\hat{i} + \hat{j} + 17\hat{k}$.The equation of the plane passing through $(x_0, y_0, z_0) = (1, 2, -3)$ is $a(x - x_0) + b(y - y_0) + c(z - z_0) = 0$.$11(x - 1) + 1(y - 2) + 17(z + 3) = 0$.$11x - 11 + y - 2 + 17z + 51 = 0$.$11x + y + 17z + 38 = 0$.

The equation of the plane passing through the point $(1, 2, -3)$ and perpendicular to the planes $3x + y - 2z = 5$ and $2x - 5y - z = 7$ is:

Similar Questions

Electric charges of $+10\,\mu C$,$+5\,\mu C$,$-3\,\mu C$,and $+8\,\mu C$ are placed at the corners of a square of side $\sqrt{2}\,m$. The potential at the centre of the square is:

The bromine atom possesses $35$ electrons. It contains $6$ electrons in $2p$ orbital,$6$ electrons in $3p$ orbital and $5$ electrons in $4p$ orbital. Which of these electrons experiences the lowest effective nuclear charge?

$A$ sufficiently long closed organ pipe has a small hole at its bottom. Initially,the pipe is empty. Water is poured into the pipe at a constant rate. The fundamental frequency of the air column in the pipe:

If $f(x) = \sin^2 \left( \frac{\pi}{8} + \frac{x}{2} \right) - \sin^2 \left( \frac{\pi}{8} - \frac{x}{2} \right)$,then the period of $f$ is

If $u=e^{x^2-y^2}$, then

Vedclass Test Series

Exam Paper Generator

Online Exam Module