Question

The projection length of a variable vector $x\hat{i}+y\hat{j}+z\hat{k}$ on the vector $\vec{p}=\hat{i}+2\hat{j}+3\hat{k}$ is 6 . Let $\ell$ be the minimum projection length of the vector $x^2\hat{i}+y^2\hat{j}+z^2\hat{k}$ on the vector $\vec{p}$, then the value of $\sqrt[3]{l^2+15^2}$ is

Answer 1

Answer: 9