Question

If a, b, care non-coplanar vectors and p = `("b" xx "c")/(["abc"]), "q" = ("c" xx "a")/(["abc"]), "r" = ("a" xx "b")/(["abc"])`, then a · p + b · q + c · r = ?

Options

• 0

• 2

• 3

• 1

Answer 1

3

Explanation:

We have, p = `("b" xx "c")/(["abc"])`

q = `("c" xx "a")/(["abc"])`

r = `("a" xx "b")/(["abc"])`

a · p + b · q + c · r

= `("a" * ("b" xx "c"))/["a b c"] + ("b" * ("c" xx "a"))/["a b c"] + ("c" * ("a" xx "b"))/["a b c"]`

= 1 + 1 + 1 = 3