The equation of the plane mid-parallel to the | vedclass

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

Question

(A) The given planes are $P_1: 2x - 3y + 6z + 21 = 0$ and $P_2: 2x - 3y + 6z - 14 = 0$.Since the planes are parallel,the mid-parallel plane will have

Vedclass · Accepted Answer

$4x - 6y + 12z + 7 = 0$

Vedclass · Answer

(A) The given planes are $P_1: 2x - 3y + 6z + 21 = 0$ and $P_2: 2x - 3y + 6z - 14 = 0$.Since the planes are parallel,the mid-parallel plane will have the same normal vector $(2, -3, 6)$.Let the equation of the mid-parallel plane be $2x - 3y + 6z + d = 0$.The constant term $d$ of the mid-parallel plane is the average of the constant terms of the two given planes,provided the coefficients of $x, y, z$ are identical.First,ensure the coefficients are the same. Here they are already the same.The constant $d$ is given by $d = \frac{d_1 + d_2}{2} = \frac{21 + (-14)}{2} = \frac{7}{2} = 3.5$.Thus,the equation is $2x - 3y + 6z + 3.5 = 0$.Multiplying by $2$ to clear the fraction,we get $4x - 6y + 12z + 7 = 0$.

The equation of the plane mid-parallel to the planes $2x - 3y + 6z + 21 = 0$ and $2x - 3y + 6z - 14 = 0$ is given by

Similar Questions

If $S$ is the set of all real values of $a$ such that a plane passing through the points $(-a^2, 1, 1), (1, -a^2, 1), (1, 1, -a^2)$ also passes through the point $(-1, -1, 1)$,then $S=$

$A$ plane passes through the point $A(2, 1, -3)$. If the distance of this plane from the origin is maximum,then its equation is

For scalars $\lambda, \mu$, if the vector equation of a plane is $r=(2+3 \lambda-\mu) \hat{i}+(1-2 \lambda+3 \mu) \hat{j}+(-2+2 \lambda+\mu) \hat{k}$, then its Cartesian equation is

The Cartesian equation of the plane $\bar{r}=(\hat{i}-\hat{j})+\lambda(\hat{i}+\hat{j}+\hat{k})+\mu(\hat{i}-2 \hat{j}+3 \hat{k})$ is

Find the coordinates of the foot of the perpendicular drawn from the origin to the plane $2x + 3y + 4z - 12 = 0$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module