Question

Prove that the two planes, 3x - 4y + 5z = 0 and 2x - y - 2z = 5 are mutually perpendicular.

Answer 1

Given equations,

3x - 4y + 5z = 0 ...(i)

2x - y - 2z = 0 ...(ii)

According to formula, a1x + b1y + c1z + d1 = 0 and a2x + b2y + c2z + d2 = 0 is perpendicular if,

a1a2 + b1b2 + c1c2 = 0

Here, a1 = 3, b1 = -4, c1 = 5

a2 = 2, b2 = -1, c2 = -2

then a1a2 + b1b2 + c1c2

= 3 x 2 + (-4) x (-1) + 5 x (-2)

= 6 + 4 - 10 = 10 - 10 = 0

Hence, eq. (i) and (ii) is perpendicular.