Question

If two adjacent sides of a square are represented by the vectors $x\overline{i}+\overline{j}+4\overline{k}$ and $3\overline{i}+y\overline{j}$ then $xy=$

• A. $1$
• B. $2$
• C. $3$
• D. $-3$

Answer 1

The correct option is D $-3$

$\begin{array}{c}\left(x\hat{i}+\hat{j}+4\hat{k}\right)\cdot \left(3\hat{i}+y\hat{j}\right)=0\\ 3x+y=0\\ \sqrt{x^2+1+16}=\sqrt{9+y^2}\\ x^2+17=9+y^2\\ 8=8x^2\\ x^2=1\\ x=1,y=-3\\ xy=-3\\ Hence,thecorrectoptionis\left(D\right)\end{array}$