Question

Given vectors a, b, c such that $\mathbf{a}.(\mathbf{b} \times \mathbf{c}) = \lambda \neq 0,$ the value of $(\mathbf{b} \times \mathbf{c}).(\mathbf{a} + \mathbf{b} + \mathbf{c})/\lambda$ is

• A. 3
• B. 1
• C. $- 3\lambda$
• D. $3/\lambda$

Answer 1

Answer: (B)

1

Answer 2

$\frac{(b \times c).(a + b + c)}{\lambda} = \frac{(b \times c).a + (b \times c).b + (b \times c).c}{\lambda}$

$= \frac{(b \times c).a + 0 + 0}{\lambda} = \frac{\lambda}{\lambda} = 1$,

($\because$Given$a.(b \times c) = \lambda = (b \times c).a$).