Q73 / 160 · TS EAMCET 2013 · Mathematics

If $\mathbf{a} \neq \mathbf{0}, \mathbf{b} \neq \mathbf{0}, \mathbf{c} \neq 0, \mathbf{a} \times \mathbf{b}=\mathbf{0}$ and $\mathbf{b} \times \mathbf{c}=0$, then $\mathbf{a} \times \mathbf{c}$ is equal to

  • A
    $b$
  • B
    $a$
  • Correct answer
    C
    $0$
  • D
    $\mathbf{i}+\mathbf{j}+\mathbf{k}$

Solution

Given,
\(a \neq 0, b \neq 0, c \neq 0\) and \(a \times b=0, b \times c=0\)
$\mathbf{a} \times \mathbf{b}=\mathbf{0} \quad \Rightarrow$ Vector $\mathbf{a}$ and $\mathbf{b}$ are parallel.
$\Rightarrow \mathbf{a}$ and $\mathbf{c}$ are also parallel.
$\Rightarrow a \times c=0$

Hence, the correct answer is option: 'C'.

Relevant Questions