Question

For any non zero vector, a, b, c a · ((b + c) × (a + b + c)] = ______.

Options

• 0

• 2[a b c]

• [a b c]

• [a c b]

Answer 1

For any non zero vector, a, b, c a · ((b + c) × (a + b + c)] = 0.

Explanation:

We have, a · ((b + c) × (a + b + c)]

= a · [(b × a + b × b + b × c + c × a + c × b +c × c)]

= a · [(b × a) + (b × c) + (c × a) + (c × b)]

= a [(b × a) + (b × c) + (c × a) - (b × c)]

= a [(b × a) + (c × a)]

= [a b a] + [a c a] = 0 + 0 = 0