Answer the following as true or false.
Two collinear vectors having the same magnitude are equal.

If $\bar{a} = \hat{i} + \hat{j} + \hat{k}$,$\bar{b} = 4\hat{i} - 2\hat{j} + 3\hat{k}$,and $\bar{c} = \hat{i} - 2\hat{j} + \hat{k}$,then the vector of magnitude $6$ units,which is parallel to the vector $2\bar{a} - \bar{b} + 3\bar{c}$,is:

Represent graphically a displacement of $40 \, km,$ $30^\circ$ west of south.

If $\bar{a}, \bar{b}, \bar{c}$ are three non-zero vectors,no two of them are collinear,$\bar{a}+2 \bar{b}$ is collinear with $\bar{c}$,and $\bar{b}+3 \bar{c}$ is collinear with $\bar{a}$,then $\bar{a}+2 \bar{b}$ is equal to:

If the vectors $\vec{a}=2 \hat{i}+p \hat{j}+4 \hat{k}$ and $\vec{b}=6 \hat{i}-9 \hat{j}+q \hat{k}$ are collinear,then the values of $p$ and $q$ are:

Let $\vec{\alpha} = (\lambda - 2) \vec{a} + \vec{b}$ and $\vec{\beta} = (4\lambda - 2)\vec{a} + 3\vec{b}$ be two given vectors where $\vec{a}$ and $\vec{b}$ are non-collinear. The value of $\lambda$ for which vectors $\vec{\alpha}$ and $\vec{\beta}$ are collinear is: