Question

The lines $\frac{x-1}{a}=\frac{y-2}{3}=\frac{z-3}{4}$
$\frac{x-2}{3}=\frac{y-3}{4}=\frac{z-4}{5}$ are coplanar. Then a =

• A. $1$
• B. $2$
• C. $-1$
• D. $-2$

Answer 1

Answer: (B)

$2$

$\begin{array}{c}\frac{x-1}{a}=\frac{y-2}{3}=\frac{z-3}{4}and\\ \frac{x-2}{3}=\frac{y-3}{4}=\frac{z-4}{5}\\ So,\left|\begin{array}{ccc}2-1& 3-2& 4-3\\ a& 3& 4\\ 3& 4& 5\end{array}\right|=0\\ \left|\begin{array}{ccc}1& 1& 1\\ a& 3& 4\\ 3& 4& 5\end{array}\right|=0\\ 1\left(15-16\right)-\left(5a-12\right)+\left(4a-9\right)=0\\ -1+12-5a+4a-9=0\\ a=2\\ optionBiscorrectanswer.\end{array}$