The values of $x$ and $y$ for which vectors $\vec{A} = (6\hat{i} + x\hat{j} - 2\hat{k})$ and $\vec{B} = (5\hat{i} - 6\hat{j} - y\hat{k})$ may be parallel are

Which of the following relations is correct?

State with reasons,whether the following algebraic operations with scalar and vector physical quantities are meaningful:
$(a)$ adding any two scalars,
$(b)$ adding a scalar to a vector of the same dimensions,
$(c)$ multiplying any vector by any scalar,
$(d)$ multiplying any two scalars,
$(e)$ adding any two vectors,
$(f)$ adding a component of a vector to the same vector.

$ABCDEF$ is a regular hexagon and forces represented in magnitude and direction by $\overrightarrow{AB}, \overrightarrow{AC}, \overrightarrow{AD}, \overrightarrow{AE}$ and $\overrightarrow{AF}$ act at point $A$. Their resultant is:

If $|\vec{A} + \vec{B}| = |\vec{A}| + |\vec{B}|$,the angle between $\vec{A}$ and $\vec{B}$ is ....... $^o$.

Three forces of $3 \ N$,$4 \ N$,and $12 \ N$ act at a point in mutually perpendicular directions. Find the magnitude of the resultant force in $N$.