(a) Position vectors of the points A, B and C as shown in the figure below are a, b and c respectively. If AC =5/4 AB, express c in terms of a and b.

Position vectors of the points $\displaystyle \mathrm{A}, \mathrm{B}$ and C as shown in the figure below are $\displaystyle \overrightarrow{\mathrm{a}}, \overrightarrow{\mathrm{b}}$ and $\displaystyle \overrightarrow{\mathrm{c}}$ respectively.

If $\displaystyle \overrightarrow{\mathrm{AC}}=\frac{5}{4} \overrightarrow{\mathrm{AB}}$, express $\displaystyle \overrightarrow{\mathrm{c}}$ in terms of $\displaystyle \overrightarrow{\mathrm{a}}$ and $\displaystyle \overrightarrow{\mathrm{b}}$.

Check whether the lines given by equations $\displaystyle \mathrm{x}=2 \lambda+2, \mathrm{y}=7 \lambda+1$, $\displaystyle \mathrm{z}=-3 \lambda-3$ and $\displaystyle \mathrm{x}=-\mu-2, \mathrm{y}=2 \mu+8, \mathrm{z}=4 \mu+5$ are perpendicular to each other or not.