Answer to Question #227897 in Physics for mcb

Question

For the vectors vec A = hat i +4 hat j -2 hat k and vec B =2 hat i - hat j +3 hat k , find the magnitude of thevector product | vec A * vec B | .

Answer 1

$$C=AB\sin{\alpha}\\A=\sqrt{1^2+4^2+2^2}=\sqrt{21}\\B=\sqrt{1^2+3^2+2^2}=\sqrt{14}\\\cos \alpha=\frac{1(2)+4(-1)+(-2)(3)}{\sqrt{21}\sqrt{14}}=-0.4666\\\alpha=117.8\degree\\C=\sqrt{21}\sqrt{14}\sin{117.8}=17.1$$