If $\overrightarrow {b} \times \overrightarrow {c} = \overrightarrow {c} \overrightarrow {a} \neq 0$, then $\overrightarrow{a} + \overrightarrow {b} = k \overrightarrow {c}$ where k is any scalar. Is it true or false .

Question

$(A)\; True$
$(B)\; False$
$(C)\; Cannot \; be \; determined$