Unit vector perpendicular to two vectors

Question

Find a unit vector perpendicular to both the vectors: $$\vec{A} = 2\hat{i}+3\hat{j}+\hat{k}$$ $$\vec{B} = \hat{i}-2\hat{j}+\hat{k}$$ I have tried to solve the question by finding unit vector along $\vec{A} \times \vec{B}$ but getting the wrong answer. Please help.

Answer 1

Only remember how you define $u\times v$ Like a determinant. $u\times v=|\begin{pmatrix} u_1 & u_2 & u_3\\ v_1& v_2 & v_3 \\ i & j & k \\ \end{pmatrix}| $