Question

Determine whether the given planes are parallel or perpendicular and in case they are neither, find the angle between them.

2x-y+3z-1=0 and 2x-y+3z+3=0

Answer 1

Given planes are

2x-y+3z-1=0 and 2x-y+3z+3=0

Here, $a_1=2,b_1=-1,c_1=3and{a}_2=2,b_2=-1,c_2=3$

$\therefore a_1{a}_2+b_1{b}_2+c_1{c}_2=2\times 2+(-1)\times (-1)+3\times 3$

$=4+1+9=14\ne 0$

Here, $\frac{a_1}{a_2}=\frac{2}{2}=1,\frac{b_1}{b_2}=\frac{-1}{-1},\frac{c_1}{c_2}=\frac{3}{3}=1$

It can be seen that $\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}$.

Thus, the given lines are parallel to each other.