Question

The equation of plane passing through the lines (x/2) = [(y – 1)/1] = [(z + 2)/2] and [(2x + 3)/4] = [(3 – y)/(– 1)] = (z/2) is ____

(A) 4x + 11y + 14z = 36

(B) 4x + 14y – 11z = 36

(C) 4x – 14y – 11z = 36

(D) 4x – 14y + 11z = 36

Answer 1

The correct option (B) 4x + 14y – 11z = 36

Explanation:

Lines: (x/2) = [(y –1)/1] = [(z + 2)/2] and

[(2x + 3)/4] = [(3 – y)/(– 1)] = (z/2)

i.e. [{x + (3/2)}/2] = [(y – 3)/1] = (z/2)

∴ vector a = (0, 1, – 2) and vector ℓ = (2, 1, 2)

also vector b = [{(– 3)/2}, 3, 0] and vector m = (2, 1, 2)

vector ℓ = vector m ⇒ lines are parallel.