Which of the following is a vector quantity?

$A$ man goes $10\,m$ towards North,then $20\,m$ towards East. The displacement is ........ $m$.

The resultant magnitude of two vectors of same magnitude is equal to the magnitude of either. The angle between the two vectors is (in $^{\circ}$)

For the resultant of two vectors $A$ and $B$ to be maximum,the angle between them should be (in $^{\circ}$)

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.

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