Q73 / 160 · AP 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, $$ a \neq 0, b \neq 0, c \neq 0 \text { and } a \times b=0, b \times c=0 $$ $\mathbf{a} \times \mathbf{b}=\mathbf{0} \quad \Rightarrow$ 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'.

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