Question

Two lines x = ay + b, z = cy + d and $x=a^{1}y+b^1,z=c^{1}y+d^1$ will be perpendicular, if and only if

• A. $a{a}^1+b{b}^1+c{c}^1=0$
• B. $(a+a^1)(b+b^1)(c+c^1)=0$
• C. $a{a}^1+c{c}^1+1=0$
• D. $a{a}^1+b^1+c{c}^1+1=0$

Answer 1

The correct option is C $a{a}^1+c{c}^1+1=0$

Lines can be written as $\frac{x-b}{a}=\frac{y}{1}=\frac{z-d}{c}and\frac{x-b^1}{a^1}=\frac{y}{1}=\frac{z-d^1}{c^1}$ which will be perpendicular if and only if $a{a}^1+1+c{c}^1=0$