The value of 'a' for which the lines 2ax - 2y + 3z = 0; x + ay + 2z = 0 and 2x + az = 0 are concurrent, is .

-2

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

-1

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is B 2
If the lines are concurrent, then
$⎛ ⎜ ⎝ \begin{matrix} 2 a & - 2 & 3 1 & a & 2 2 & 0 & a \end{matrix} ∣ ∣ ∣ ∣ = 0 \Rightarrow 2 a (a^{2} - 0) + 2 (a - 4) + 3 (0 - 2 a) = 0 \Rightarrow 2 a^{3} + 2 a - 8 + 0 - 6 a = 0 \Rightarrow 2 a^{3} - 4 a - 8 = 0 \Rightarrow a^{3} - 2 a - 4 = 0 \Rightarrow a^{3} - 2 a^{2} + 2 a^{2} - 4 a + 2 a - 4 = 0 \Rightarrow a^{2} (a - 2) + 2 a (a - 2) + 2 (a - 2) = 0 \Rightarrow (a - 2) (a^{2} + 2 a + 2) = 0 \Rightarrow a = 2$

Suggest Corrections

Similar questions

2 a x - 2 y + 3 z = 0, x + a y + 2 z = 0 and 2 x + a z = 0

a

2 a x - 2 y + 3 z = 0, x + a y + 2 z = 0, 2 x + a z = 0

a

k x + 2 y + 2 = 0,

2 x + k y + 3 = 0,

3 x + 3 y + k = 0

Join BYJU'S Learning Program