Answer
a) $ \vec D=7\;\hat i−7\;\hat j $
b) See the figure below.
c) $9.9,\;315^\circ$
Work Step by Step
a) We need to find $\vec D$ in component forms whereas
$$\vec D=\vec A-\vec B$$
Plugging the known;
$$\vec D=(4\;\hat i−2\;\hat j)-(−3\;\hat i+5\;\hat j )=4\;\hat i+3\;\hat i−2\;\hat j-5\;\hat j$$
$$\boxed{\vec D=7\;\hat i−7\;\hat j}$$
b) See the figure below. We drew the 3 vectors there.
c) The magnitude of $\vec D$ is given by applying the Pythagorean theorem.
$$|\vec D|=\sqrt{D_x^2+D_y^2}=\sqrt{7^2+(-7)^2}=\color{red}{\bf 9.9}$$
and its direction is given by
$$\tan\alpha_D=\dfrac{D_y}{D_x}$$
Thus,
$$\alpha_D=\tan^{-1}\left[\dfrac{D_y}{D_x}\right]=\tan^{-1}\left[\dfrac{-7}{7}\right]=\bf -45^\circ$$
Thus,
$$\alpha_D=\color{red}{\bf 315^\circ}$$
