A solution of the vector equation $\vec r×\vec b =\vec a×\vec b$, where $\vec a,\vec b$ are two given vectors, is where λ is a parameter.
Answer & explanation
Correct answer: option 2
We have,
$\vec r×\vec b =\vec a×\vec b$
$⇒\vec r×\vec b -\vec a×\vec b=\vec 0$
$⇒(\vec r-\vec a)×\vec b=\vec 0$
$⇒\vec r-\vec a$ is parallel to $\vec b$
$⇒\vec r-\vec a=λ\vec b$ for some scalar λ
$⇒\vec r=\vec a+λ\vec b$ is the required solution.