The line x + y = 4 cuts the line joining P(-1, 1) and Q(5, 7) at R. What is PR ∶ RQ equal to ?

What is the sum of the intercepts of the line whose perpendicular distance from origin is 4 units and the angle which the normal makes with positive direction of x-axis is 15°?

What is the length of projection of the vector $\rm \hat{i}+2 \hat{j}+3 \hat{k}$ on the vector $\rm2 \hat{i}+3 \hat{j}-2 \hat{k}$ ?

If $\rm (\vec{a} \times \vec{b})^2+(\vec{a} \cdot \vec{b})^2=144$ and $\rm|\vec{b}|=4 $, then what is the value of $\rm|\vec{a}|$ ?