If the three planes px + 4y + z = 0, 2y + 3z – 1 = 0 and 3x – qz + 2 = 0 have a common line then the value of p + q is___

Open in App

Solution

Since the three plane meet at one line, the given system of equation have infinite no. of solutions
$Δ = ∣ ∣ ∣ ∣ \begin{matrix} p & 4 & 1 0 & 2 & 3 3 & 0 & - q \end{matrix} ∣ ∣ ∣ ∣ = 0 \Rightarrow p q = 15$
$Δ_{1} = ∣ ∣ ∣ ∣ \begin{matrix} 0 & 4 & 1 1 & 2 & 3 - 2 & 0 & - q \end{matrix} ∣ ∣ ∣ ∣ = 0 \Rightarrow q = 5 \Rightarrow p = 3$

Suggest Corrections

Similar questions

p

q

p z + 4 y + z = 0, 2 y + 3 z = 1

3 x - q z = - 2

\sqrt{q^{2} - p^{2}}

2 x + p y + 6 z = 8 x + 2 y + q z = 5 x + y + 3 z = 4

If the equation $x^{2} + p x + q = 0$ and $x^{2} + q x + p = 0$ , have a common root, then p + q + 1 =

\frac{x - 1}{3} = \frac{y - 3}{5} = \frac{z - 4}{2}

2 x - y + z + 3 = 0

L .

7 x + p y + q z + r = 0

(p, q, r \in R)

L

2 x - y + z + 3 = 0,

(p + 3 q + r)

3 x + 4 y + z = 0

x - 2 y - 3 z = 5

Join BYJU'S Learning Program