Let (alpha, beta, gamma) be the image of the | vedclass

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

Question

(A) The formula for the image $(\alpha, \beta, \gamma)$ of a point $(x_1, y_1, z_1)$ in the plane $ax + by + cz + d = 0$ is given by:$\frac{\alpha - x

Vedclass · Accepted Answer

$10$

Vedclass · Answer

(A) The formula for the image $(\alpha, \beta, \gamma)$ of a point $(x_1, y_1, z_1)$ in the plane $ax + by + cz + d = 0$ is given by:$\frac{\alpha - x_1}{a} = \frac{\beta - y_1}{b} = \frac{\gamma - z_1}{c} = -2 \left( \frac{ax_1 + by_1 + cz_1 + d}{a^2 + b^2 + c^2} \right)$Given point $P(2, 3, 5)$ and plane $2x + y - 3z - 6 = 0$,we have $a=2, b=1, c=-3, d=-6$:$\frac{\alpha - 2}{2} = \frac{\beta - 3}{1} = \frac{\gamma - 5}{-3} = -2 \left( \frac{2(2) + 1(3) - 3(5) - 6}{2^2 + 1^2 + (-3)^2} \right)$Calculate the value inside the bracket:$\frac{4 + 3 - 15 - 6}{4 + 1 + 9} = \frac{-14}{14} = -1$So,the ratio is $-2(-1) = 2$:$\frac{\alpha - 2}{2} = 2 \implies \alpha - 2 = 4 \implies \alpha = 6$$\frac{\beta - 3}{1} = 2 \implies \beta - 3 = 2 \implies \beta = 5$$\frac{\gamma - 5}{-3} = 2 \implies \gamma - 5 = -6 \implies \gamma = -1$Therefore,$\alpha + \beta + \gamma = 6 + 5 - 1 = 10$.

Let $(\alpha, \beta, \gamma)$ be the image of the point $P (2, 3, 5)$ in the plane $2x + y - 3z = 6$. Then $\alpha + \beta + \gamma$ is equal to

Similar Questions

If the foot of the perpendicular from $(0,0,0)$ to the plane is $(1,2,2)$,then the equation of the plane is

The distance of a point $(1, 2, -1)$ from the plane $x - 2y + 4z + 10 = 0$ is

If the plane $2x + 3y + 5z = 1$ intersects the coordinate axes at the points $A, B, C$,then the centroid of $\triangle ABC$ is

The equations of planes parallel to the plane $x+2y+2z+8=0$,which are at a distance of $2$ units from the point $(1,1,2)$ are

If the foot of the perpendicular drawn from the origin to the plane is $(3, 2, 1)$,then the equation of the plane is

Vedclass Test Series

Exam Paper Generator

Online Exam Module