Question

The direction ratios of two perpendicular lines are $k,-6,-2$ and $k-1,k,4$, then value of $k$ are

• A. $8,-1$
• B. $2,3$
• C. $8,1$
• D. $-8,-1$

Answer 1

The correct option is A $8,-1$

Given,

Given direction ratios of perpendicular lines $k,-6,-2$ and $k-1,k,4$ for perpendicular line,

the dot product will be zero

$\therefore k(k-1)-6\left(k\right)-2\left(4\right)=0$

$\Rightarrow k^2-k-6k-8=0$

$\Rightarrow k^2-7k-8=0\Rightarrow k^2-8k+k-8=0$

$\Rightarrow (k+1)(k-8)=0$

$k=8,-1$