Question

For what value of λ do the planes x – y + z + 1 = 0, λx + 3y + 2z – 3 = 0, 3x + λy + z – 2 = 0 form a triangular prism ?

(a) 4

(b) –3

(c) 2

(d) \(\frac{16}3\)

Answer 1

Correct option is (a) 4

Given planes form a prism if r = 2 & s = 3

i.e. |A| = 0 & none of △₁, △₂, △₃ is zero.

From (1), (2), (3) & (4) we find if λ = 4, |A| = 0 & none of △₁, △₂, △₃ zero.

\(\therefore\) For λ = 4 the given planes form a triangular prism.