Question

The value of a, for which the points A,B, C with position vectors $2\overline{i}-\overline{j}+\overline{k},\overline{i}-3\overline{j}-5\overline{k}anda\overline{i}-3\overline{j}+\overline{k}$ respectively are the vertices of a right angled triangle with $\angle C=\frac{\pi }{2}$ are`

• A. -2 or 1
• B. 2 or -1
• C. 2 or 1
• D. -2 or -1

Answer 1

The correct option is C 2 or 1

$\begin{array}{c}\overrightarrow{CA}.\overrightarrow{CB}=0\\ \overrightarrow{CA}=\left(2-a\right)\hat{i}-2\hat{j}\\ \overrightarrow{CB}=\left(1-a\right)\hat{i}-6\hat{j}\\ a^2-3a+2=0\\ \left(a-2\right)\left(a-1\right)=0\\ a=1,2\end{array}$