Question

If $\lambda x+4y+5z=7$ and $4x+4\lambda y+10z-14=0$ represent the same plane, then the value of $\lambda$ is equal to

Answer 1

Given equations represent the same plane
$\therefore \frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}=\frac{d_1}{d_2}\Rightarrow \frac{\lambda }{4}=\frac{5}{10}\Rightarrow \lambda =2$