Question

Two lines L₁: (x – x₁)/a₁ = (y – y₁)/b₁ = (z – z₁)/c₁

and L₂: (x – x₂)/a₂ = (y – y₂)/b₂ = (z – z₂)/c₂ are coplanar if

|((x₂ - x₁,y₂ - y₁,z₂ - z₁),(a₁,b₁,c₁),(a₂,b₂,c₂))| = 0

If two lines (x – 1)/2 = (y – 2)/3 = (z – 3)/4 and (x – 4)/5 = (y – 1)/2 = z are coplanar, the point of intersection is

(a) (1, 1, 1)

(b) (1, –1, –1)

(c) (–1, –1, –1)

(d) (1, 1, –1)

Answer 1

Answer is (c) (–1, –1, –1)

Let

Hence, the point of intersection is (– 1, –1, –1).