If $|\vec{c}|^2 = 60$ and $\vec{c} \times (\hat{i} + 2\hat{j} + 5\hat{k}) = \vec{0}$,then a value of $\vec{c} \cdot (-7\hat{i} + 2\hat{j} + 3\hat{k})$ is

The line joining the points $6 \overrightarrow{a}-4 \overrightarrow{b}+4 \overrightarrow{c}$ and $-4 \overrightarrow{c}$ and the line joining the points $-\overrightarrow{a}-2 \overrightarrow{b}-3 \overrightarrow{c}$ and $\overrightarrow{a}+2 \overrightarrow{b}-5 \overrightarrow{c}$ intersect at:

$A$ vector $\vec{r}$ is inclined at equal angles to the three axes. If the magnitude of $\vec{r}$ is $2 \sqrt{3}$ units,find $\vec{r}$.

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

If $\vec{a}=(p, -2, 5)$ and $\vec{b}=(1, q, -3)$ are collinear vectors,then:

If $m_1, m_2, m_3$ and $m_4$ are respectively the magnitudes of the vectors $\overrightarrow{a}_1=2 \hat{i}-\hat{j}+\hat{k}$, $\overrightarrow{a}_2=3 \hat{i}-4 \hat{j}-4 \hat{k}$, $\overrightarrow{a}_3=\hat{i}+\hat{j}-\hat{k}$ and $\overrightarrow{a}_4=-\hat{i}+3 \hat{j}+\hat{k}$, then the correct order of $m_1, m_2, m_3$ and $m_4$ is