Let a , b , c be three non-coplanar vectors and p , q , r defined by the relations p = b c [ a ~b c ] , q = c a [ a ~b c ] , r = a b [ a ~b c ] then the value of the expression ( a + b ) p +( b + c ) q +( c + a ) r is equal to

Step-by-step solution

aligned p ( a + b ) & = p a + p b & = ( b c ) a [ a b c ] + ( b c ) b [ a b c ] & = [ b c a ] [ a b c ] + [ b c b ] [ a b c ] & =1+0=1 aligned Similarly, q ( b + c )=1 and r ( a + c )=1 aligned & ( a + b ) p +( b + c ) q +( c + a ) r & =1+1+1 & =3 aligned