If a, b, c are three non - coplanar vectors and p, q, r are vectors defined by the relations $p=\frac{b \times c}{[abc]}, q=\frac{c \times a}{[abc]}, r=\frac{a \times b}{[abc]}$ then the value of expression (a + b).p + (b + c).q + (c + a).r is equal to

3

$(\bar{a}+\bar{b}) . \bar{p}=\frac{(\bar{a}+\bar{b}) .(\bar{b} \times \bar{c})}{[\bar{a} \bar{b} \bar{c}]}=\frac{\bar{a} .(\bar{b} \times \bar{c})}{[\bar{a} \bar{b} \bar{c}]}=1$

Hence the given scalar expression = 1 + 1 + 1 = 3.

Hence (4) is correct answer.