3.1 vectors — Physics STD 11 Science — Question

$\vec{A}=2 \hat{\imath}-3 \hat{\jmath}+4 \hat{k}$

$\vec{B}=4 \hat{\imath}+\hat{\jmath}+2 \hat{k}$

$|\vec{A} \times \vec{B}|=$ ?

$|\vec{A} \times \vec{B}|=? \quad\left|\begin{array}{ccc}\hat{\imath} & \hat{\jmath} & \hat{k} \\ 2 & -3 & 4 \\ 4 & 1 & 2\end{array}\right|$

$=\hat{\imath}(-6-4)-\hat{\jmath}(4-16)+k(2+12)$

$=-10 \hat{\imath}+12 \hat{\jmath}+14 \hat{k}$

$|\vec{A} \times \vec{B}|=\sqrt{(-10)^2+(12)^2+(14)^2}$

$=\sqrt{\frac{100+144+196}{\sqrt{440}}}$

$=\sqrt{440}=2 \sqrt{110}$