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Question: If the planes \(3x - 2y + 2z + 17 = 0\)and \(4x + 3y - kz = 25\) are mutually perpendicular , then \...

If the planes 3x−2y+2z+17=03x - 2y + 2z + 17 = 0and 4x+3y−kz=254x + 3y - kz = 25 are mutually perpendicular , then k=k =

A

3

B

– 3

C

9

D

– 6

Answer

3

Explanation

Solution

Obviously, 3×4+(−2)×3+2×(−k)=03 \times 4 + ( - 2 ) \times 3 + 2 \times ( - k ) = 0

⇒12−6−2k=0⇒k=3\Rightarrow 12 - 6 - 2 k = 0 \Rightarrow k = 3