Question

Let a, b and c be vectors with magnitudes 3, 4 and 5 respectively and a + b + c = 0, then the values of a.b + b.c + c.a is

• A. 47
• B. 25
• C. 50
• D. – 25

Answer 1

Answer: (D)

– 25

Answer 2

$\because$ $\mathbf{a} + \mathbf{b} + \mathbf{c} = 0$

Squaring both sides, we get

$|\mathbf{a}|^{2} + |\mathbf{b}|^{2} + |\mathbf{c}|^{2} + 2(\mathbf{a}.\mathbf{b} + \mathbf{b}.\mathbf{c} + \mathbf{c}.\mathbf{a}) = 0$

$\Rightarrow 2(\mathbf{a}.\mathbf{b} + \mathbf{b}.\mathbf{c} + \mathbf{c}.\mathbf{a}) = - (9 + 16 + 25)$

$\Rightarrow \mathbf{a}.\mathbf{b} + \mathbf{b}.\mathbf{c} + \mathbf{c}.\mathbf{a} = - 25.$