If $\vec{a}=(2x+y)\hat{i}+3\hat{j}+9\hat{k}$ and $\vec{b}=2\hat{i}+\hat{j}-(x-y)\hat{k}$ are two collinear vectors,then $x^3+27y^3=$

If $\vec{a}$ is a nonzero vector of magnitude $a$ and $\lambda$ is a nonzero scalar,then $\lambda \vec{a}$ is a unit vector if

If $\vec{a}, \vec{b}, \vec{c}$ are three vectors such that $|\vec{a}|=3, |\vec{b}|=5, |\vec{c}|=7$,then $|\vec{a}-\vec{b}|^2+|\vec{b}-\vec{c}|^2+|\vec{c}-\vec{a}|^2$ does not exceed:

If $\vec{a}$ and $\vec{b}$ are the position vectors of $A$ and $B$,respectively,find the position vector of a point $C$ in $BA$ produced such that $BC = 1.5 BA$.

Write two different vectors having the same direction.

Classify the following measure as a scalar or a vector:
$40^{o}$