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)  16/3

Answer 1

Correct option  (a) 4

Explanation:

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

i.e. |A| = 0 & none of  Δ₁ , Δ₂ , Δ₃ is zero.

From (1), (2), (3) & (4) we find if λ = 4, |A| = 0 & none of Δ₁ , Δ₂ , Δ₃ zero.

For λ = 4 the given planes form a triangular prism