Classify the following as scalar and vector quantities:
Force

If $|a| = 3, |b| = 4$ and $|a + b| = 5,$ then $|a - b| = $

If the points with position vectors $\alpha \hat{i} + 10 \hat{j} + 13 \hat{k}$,$6 \hat{i} + 11 \hat{j} + 11 \hat{k}$,and $\frac{9}{2} \hat{i} + \beta \hat{j} - 8 \hat{k}$ are collinear,then $(19 \alpha - 6 \beta)^2$ is equal to $...........$.

If $a, b, c$ are three non-coplanar vectors such that $a + b + c = \alpha d$ and $b + c + d = \beta a$,then $a + b + c + d$ is equal to

Two vectors $u$ and $v$ are parallel if and only if

Let $u$ and $v$ be two vectors in $R^2$. If $|u+v|^2=2(|u|^2+|v|^2)$,then .....