Question

A and b are two vector and theta is the angle between them |a×b|

Answer 1

A and B are two vectors and theta is the angle between them. If |A×B|= underoot 3 of (A.B), what is the value of theta?

|A×B|=a*b*sin(theta) where |A|=a, and |B|=b

So, |A×B|=(A.B)^(1/3)=[a*b*cos(theta)]^(1/3)=a*b*sin(theta)

[sin(theta)]^3=cos(theta) or [sin(theta)]^2*tan(theta)=1 or tan(theta)=1/[sin(theta)]^2 or sin(theta)={1+[sin(theta)]^4}^-0.5

[sin(theta)]^2*{1+[sin(theta)]^4]=1 or

sin(theta)]^6+[sin(theta)]^2–1=0

[sin(theta)]^2=[(0.5*27+209.25^0.5)^(1/3)+(0.5*27-209.25^0.5)^(1/3)]/3

theta = 55.6932°

Hope this help you

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