Question

The value of k such that the line (x - 4)/1 = (y - 2)/1 = (z - k)/2 lies in the plane 2x - 4y + z - 7 = 0 is

(A) 7 

(B) −7 

(C) no real value 

(D) 4

Answer 1

Correct option is (A) 7

Explanation :

Every point on the given line is of the form (4 + λ, 2 + λ, k + 2λ), where λ ∈ R. This point lies in the plane

2x - 4y + z - 7 = 0

So

2(4 + λ) - 4(2 + λ) + l(k + 2λ) - 7 = 0

for all λ ∈ R

In particular, for λ = 0, we have

8 - 8 + k - 7 = 0 

k = 7

Note that the point (4, 2, k) lies on the given line and hence it lies in the given plane. So

2(4) - 4(2) + k - 7 = 0

k = 7