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
$b$
$a$
$0$
$\mathbf{i}+\mathbf{j}+\mathbf{k}$
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.
$\Rightarrow a \times c=0$