Question

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

• A. $3$
• B. $-1$
• C. $1$
• D. $-3$

Answer 1

The correct option is D $-3$

Let, adjacent sides of square are represented by ${\overrightarrow{S}}_1=(x\hat{i}+\hat{j}+4\hat{k})$ and ${\overrightarrow{S}}_2=(y\hat{i}+3\hat{j}).$
Since adjacents sides of any square are perpendicular to each other.
$\Rightarrow {\overrightarrow{S}}_1\cdot {\overrightarrow{S}}_2=0$
$\Rightarrow (x\hat{i}+\hat{j}+4\hat{k})\cdot (y\hat{i}+3\hat{j})=0$
$\Rightarrow xy+3=0$
$\Rightarrow xy=-3$