Question

Let $\overrightarrow{OP}=\frac{\alpha-1}{\alpha}\hat{i}+\hat{j}+\hat{k},\overrightarrow{OQ}=\hat{i}+\frac{\beta-1}{\beta}\hat{j}+\hat{k}$ and $\overrightarrow{OR}=\hat{i}+\hat{j}+\frac{1}{2}\hat{k}$ be three vector where α, β ∈ R - {0} and 0 denotes the origin. If $(\overrightarrow{OP}\times\overrightarrow{OQ}).\overrightarrow{OR}=0$ and the point (α, β, 2) lies on the plane 3x + 3y - z + l = 0, then the value of l is _______.

Answer 1

The correct answer is: 5.