Question

Show that the lines $\frac{x-1}{2}=\frac{y-2}{3}=\frac{z-3}{4}$ and $\frac{x+1}{1}=\frac{y+2}{2}=\frac{z+3}{-2}$ are perpendicular.

Answer 1

$\frac{x-1}{2}=\frac{y-2}{3}=\frac{z-3}{4}$ & $\frac{x+1}{1}=\frac{y+2}{2}=\frac{z+3}{-2}$

for perpendicular $(a_1{a}_2+b_1{b}_2+c_1{c}_2=0$

Here, $a_1=2,a_2=1$

$b_1=3,b_2=2$

$c_1=4,c_2=-2$

$=a_1{a}_2+b_1{b}_2+c_1{c}_2$

$=2+6-8$

$=8-8$

$=0$

Hence, we can say that both the lines are perpendicular.