Physics - Vectors Question with Solution | TestHub

Vector $\vec{P}=a\hat{i}+a\hat{j}+3\hat{k}$ and vector $\vec{Q}=a\hat{i}-2\hat{j}-\hat{k}$. If two vectors are perpendicular to each other, then $$\vec{P}\cdot \vec{Q}=0\text{ or }(a\hat{i}+a\hat{j}+3\hat{k})\cdot (a\hat{i}-2\hat{j}-\hat{k})=0$$ or $a^2-2a-3=0$. Solving this quadratic equation, we get $a=3$ or -1 . Therefore positive value of $a$ is 3 .