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 $x^3+27y^3=$

Let $A, B, C, D$ be the points in the plane with position vectors $\vec{a} = -2\hat{i} - \hat{j}$, $\vec{b} = 4\hat{i}$, $\vec{c} = 3\hat{i} + 3\hat{j}$, and $\vec{d} = -3\hat{i} + 2\hat{j}$ respectively. Then $ABCD$ is:

If the vectors $\hat{i}+2 \hat{j}+x \hat{k}$ and $y \hat{i}+6 \hat{j}+4 \hat{k}$ are collinear,then the values of $x$ and $y$ are respectively,

Classify the following physical quantity as a scalar or a vector:
$10 \, g/cm^3$

In the given figure (a square),identify the co-initial vectors.

Let $a = \hat{i} + x \hat{j} + \hat{k}$,$b = \hat{i} + \hat{j} + \hat{k}$ and $|a + b| = |a| + |b|$,then