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The angles between three non-zero and non coplanar vectors a,b and c are α between b and c and β between c and a and γ between a and b. The vector u and v are defined by u=(aXb)Xc; v=aX(bXc). If u is perpendicular to v, then show that either a is perpendicular to c or cos β=cos α.cos γ .

The angles between three non-zero and non coplanar vectors a,b and c are 


α between b and c


and β between c and a


and γ between a and b.


The vector u and v are defined by u=(aXb)Xc;


v=aX(bXc).


If u is perpendicular to v, then show that either


a is perpendicular to c


or cosβ=cosα.cosγ .

Grade:12

1 Answers

azeem khan
32 Points
8 years ago

on solving weget vector u=c((vector b)acosb)-b(vector a)cosa)) & vector v=a((vector b)ccosb-(vector c)bcosg). then take dot product of vector u&v & then we get cosb=cosacosg

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