The number of vectors of unit length perpendicular to both the vectors $\vec{a}=\hat{i}+2\hat{j}+3\hat{k}$ and $\vec{b}=\hat{i}-\hat{j}+3\hat{k}$ is/are :

two

The correct answer is Option (2) → two

The number of unit vectors perpendicular to both the vector $\vec{a}=\hat{i}+2\hat{j}+3\hat{k}$ and $\vec{b}=\hat{i}-\hat{j}+3\hat{k}$ are,

$\frac{(\vec{a}×\vec{b})}{|\vec{a}×\vec{b}|}$ and $\frac{(\vec{b}×\vec{a})}{|\vec{b}×\vec{a}|}$

∴ The number is 2 always.