Correct Answer - Option 1 : 1
Concept:
For the points (x1, y1, z1), (x2, y2, z2) and (x3, y3, z3) to be collinear
\(\rm \begin{vmatrix} x_1 & y_1 &z_1 \\ x_2& y_2& z_2 \\ x_3& y_3& z_3 \end{vmatrix} = 0\)
Calculation:
The given points are (1, 3, -2), (2, λ, 1) and (3, 4, -1)
The equation of the plane will be
\(\rm \begin{vmatrix} 1 &3 &-2\\ 2& λ& 1\\ 3&4& -1 \end{vmatrix} = 0\)
⇒ 1(-λ - 4) - 3(-2 - 3) + (-2)(8 - 3λ) = 0
⇒ 5λ - 4 + 15 - 16 = 0
⇒ 5λ = 5
⇒ λ = 1
