Answer to Question #227897 in Physics for mcb

Question #227897

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 | .



1
Expert's answer
2021-08-23T12:41:53-0400
C=ABsinαA=12+42+22=21B=12+32+22=14cosα=1(2)+4(1)+(2)(3)2114=0.4666α=117.8°C=2114sin117.8=17.1C=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


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