List of top Mathematics Questions on Multiplication of a Vector by a Scalar asked in KEAM

If \( \alpha, \beta, \gamma \) are the angles made by $$ \frac{x-1}{3} = \frac{y+1}{2} = -\frac{z}{1} \text{ with the coordinate axes, then } $$ \((\cos\alpha, \cos\beta, \cos\gamma) = \) 

Let $a =\hat{ i }-2 \hat{ j }+3 \hat{ k }$. If $b$ is a vector such that $a \cdot b =| b |^{2}$ and $| a - b |=\sqrt{7}$, then $| b |$ is equal to