Question-11 The values of k for which lines kx+2y+2= 0, 2x+ ky + 3= 0 and 3x + 3y + k =0 are concurrent
A) {2, 3, 5}
B) {2, 3, -5}
C) {3, -5}
D) {-5}
Answer: C) {3, -5}
Explanation
Given: Three lines kx+2y+2= 0, 2x+ ky + 3= 0 and 3x + 3y + k =0
If we observe its coefficients, they are not proportional for all k except 2 .
For three non-parallel lines are concurrent if \triangle = 0.
\begin{aligned} & \left|\begin{array}{lll} a_{1} & b_{1} & c_{1} \\ a_{2} & b_{2} & c_{2} \\ a_{3} & b_{3} & c_{3} \end{array}\right|=0 \\ & \Rightarrow\left|\begin{array}{lll} k & 2 & 2 \\ 2 & k & 3 \\ 3 & 3 & k \end{array}\right|=0 \end{aligned}k = 2, 3, -5
But for k = 2, lines are parallel.
k = 3, -5