If a, b, c are the three non-coplanar vectors and p, q, r are defined by the relations \[\mathbf{p}=\frac{\mathbf{b}\times \mathbf{c}}{[\mathbf{a}\,\mathbf{b}\,\mathbf{c}]},\,\,\mathbf{q}=\frac{\mathbf{c}\times \mathbf{a}}{[\mathbf{a}\,\mathbf{b}\,\mathbf{c}]},\,\,\mathbf{r}=\frac{\mathbf{a}\times \mathbf{b}}{[\mathbf{a}\,\mathbf{b}\,\mathbf{c}]}\] then (a+b) . p +(b+c) . q +(c+a) . r = [IIT 1988; BIT Mesra 1996; AMU 2002]

If a, b, c are the three non-coplanar vectors and p, q, r are defined

1.	If a, b, c are the three non-coplanar vectors and p, q, r are defined by the relations \[\mathbf{p}=\frac{\mathbf{b}\times \mathbf{c}}{[\mathbf{a}\,\mathbf{b}\,\mathbf{c}]},\,\,\mathbf{q}=\frac{\mathbf{c}\times \mathbf{a}}{[\mathbf{a}\,\mathbf{b}\,\mathbf{c}]},\,\,\mathbf{r}=\frac{\mathbf{a}\times \mathbf{b}}{[\mathbf{a}\,\mathbf{b}\,\mathbf{c}]}\] then (a+b) . p +(b+c) . q +(c+a) . r = [IIT 1988; BIT Mesra 1996; AMU 2002]
A.	0
B.	1
C.	2
D.	3
Answer» E.

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