[3×2]
(a)[2.0]
If $\vec{a}$ and $\vec{b}$ are perpendicular vectors, $|\vec{a} + \vec{b}| = 13$ and $|\vec{a}| = 5$, find the value of $|\vec{b}|$.
(b)[2.0]
Find the length of the perpendicular from origin to the plane $\vec{r} \cdot (3\hat{i} - 4\hat{j} - 12\hat{k}) + 39 = 0$.
(c)[2.0]
Find the angle between the two lines $2x = 3y = -z$ and $6x = -y = -4z$.
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