Question

The equation of the plane through (1, 2, 3) and parallel to the plane $2x + 3y - 4z = 0$is

• A. $2x + 3y + 4z = 4$
• B. $2x + 3y + 4z + 4 = 0$
• C. $2x - 3y + 4z + 4 = 0$
• D. $2x + 3y - 4z + 4 = 0$

Answer 1

Answer: (D)

$2x + 3y - 4z + 4 = 0$

Answer 2

Plane parallel to the plane $2 x + 3 y - 4 z = 0$ is

$2 x + 3 y - 4 z + k = 0$ .....(i)

Also plane (i) is passing through (1, 2, 3)

$\therefore$ $( 2 ) ( 1 ) + ( 3 ) ( 2 ) - ( 4 ) ( 3 ) + k = 0 \Rightarrow k = 4$

$\therefore$ Required plane is $2 x + 3 y - 4 z + 4 = 0$.