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For two non zero vector a and b ,prove that (a*b)^2=(ab)^2-(a.b)^2.where magnitude of vector a is a and vector b is b?

For two non zero vector a and b ,prove that (a*b)^2=(ab)^2-(a.b)^2.where magnitude of vector a is a and vector b is b?

Grade:12

1 Answers

Arun
25763 Points
2 years ago
Dear student
 
LHS
 
(a * b ) = a^2 b^2 sin^2 theta
 
RHS
(ab)^2 – (a.b)^2 = a^2 b^2 (1 – cos^2 theta) = a^2 b^2 sin^2 theta
 
hence proved

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