Question

If the straight lines (x – 1)/2 = (y + 1)/k = z/2 and (x + 1)/5 = (y + 1)/2 = z/k are coplanar, the planes containing these two lines is (are) 

(a) y + 2z = –1 

(b) y + z = –1 

(c) y – z = –1 

(d) y – 2z = –1

Answer 1

Answer is (b) y + z = –1

Since given lines are coplanar, so we get

k² – 4 = 0

k = ±2

The equation of the plane containing these two lines is

(x – 1)(k² – 4) – (y + 1)(2k – 10) + z(4 – 5k) = 0 

–(y + 1)(2k – 10) + z(4 – 5k) = 0 

–(y + 1)(±4 – 10) + (4 – ±10) = 0

Taking positive sign, we get

(y + 1) – z = 0 

y – z = –1

Taking negative sign, we get

– (y + 1)(– 14) + 14z = 0 

(y + 1) + z = 0 

y + z = – 1