If the planes 3x - 2y + 2z + 17 = 0 and 4x + | vedclass

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

Question

(A) Two planes $a_1x + b_1y + c_1z + d_1 = 0$ and $a_2x + b_2y + c_2z + d_2 = 0$ are perpendicular if and only if $a_1a_2 + b_1b_2 + c_1c_2 = 0$.Given

Vedclass · Accepted Answer

$3$

Vedclass · Answer

(A) Two planes $a_1x + b_1y + c_1z + d_1 = 0$ and $a_2x + b_2y + c_2z + d_2 = 0$ are perpendicular if and only if $a_1a_2 + b_1b_2 + c_1c_2 = 0$.Given the equations of the planes are $3x - 2y + 2z + 17 = 0$ and $4x + 3y - kz - 25 = 0$.Here,$a_1 = 3, b_1 = -2, c_1 = 2$ and $a_2 = 4, b_2 = 3, c_2 = -k$.Substituting these values into the condition for perpendicularity:$(3)(4) + (-2)(3) + (2)(-k) = 0$$12 - 6 - 2k = 0$$6 - 2k = 0$$2k = 6$$k = 3$.

If the planes $3x - 2y + 2z + 17 = 0$ and $4x + 3y - kz = 25$ are mutually perpendicular,then $k = $

Similar Questions

In space,the equation $by + cz + d = 0$ represents a plane perpendicular to the plane:

The equation of the plane in normal form passing through the point $A(\vec{a})$,parallel to a vector $\vec{b}$ and containing a vector $\vec{c}$ is

The mirror image of the point $P(-1, 2, -4)$ in the plane $x - y - 2z + 1 = 0$ is

$A$ plane $E_{1}$ makes intercepts $1, -3, 4$ on the coordinate axes. The equation of a plane parallel to plane $E_{1}$ and passing through $(2, 6, -8)$ is

The image point of $(1, 3, 4)$ in the plane $2x - y + z + 3 = 0$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module