If \[\mathbf{p}=\frac{\mathbf{b}\times \mathbf{c}}{[\mathbf{a}\,\mathbf{b}\,\mathbf{c}]},\,\,\mathbf{q}=\frac{\mathbf{c}\times \mathbf{a}}{[\mathbf{a}\,\mathbf{b}\,\mathbf{c}]},\,\,\mathbf{r}=\frac{\mathbf{a}\times \mathbf{b}}{[\mathbf{a}\,\mathbf{b}\,\mathbf{c}]},\,\,\]where a, b, c are three non-coplanar vectors, then the value of \[(\mathbf{a}+\mathbf{b}+\mathbf{c})\,.\,(\mathbf{p}+\mathbf{q}+\mathbf{r})\] is given by [MNR 1992; UPSEAT 2000]

If \[\mathbf{p}=\frac{\mathbf{b}\times \mathbf{c}}{[\mathbf{a}\,\mathb

1.	If \[\mathbf{p}=\frac{\mathbf{b}\times \mathbf{c}}{[\mathbf{a}\,\mathbf{b}\,\mathbf{c}]},\,\,\mathbf{q}=\frac{\mathbf{c}\times \mathbf{a}}{[\mathbf{a}\,\mathbf{b}\,\mathbf{c}]},\,\,\mathbf{r}=\frac{\mathbf{a}\times \mathbf{b}}{[\mathbf{a}\,\mathbf{b}\,\mathbf{c}]},\,\,\]where a, b, c are three non-coplanar vectors, then the value of \[(\mathbf{a}+\mathbf{b}+\mathbf{c})\,.\,(\mathbf{p}+\mathbf{q}+\mathbf{r})\] is given by [MNR 1992; UPSEAT 2000]
A.	3
B.	2
C.	1
D.	0
Answer» B. 2

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