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 .
solution) Given that u=(axb)xc, v=ax(bxc), both the vectors are equal in magnitude because of the associated law, and u.v=0, therefore it must be true that a.c=0, because excluding a and c , b is not situated at right angles so angle between a and c is 90.