Question Type 1: Finding a vector given two points in 2D Exercises

Write the vector equation of the line through $A(0,0)$ and $B(2,3)$ in the form $\mathbf{r} = \mathbf{a} + t\mathbf{d}$.

Given $A(0,0)$, $B(3,4)$ and $C(5,1)$, find $\overrightarrow{AB}+\overrightarrow{BC}$.

In parallelogram $ABCD$, $A(1,2)$, $B(4,2)$ and $D(1,6)$. Find the vector $\overrightarrow{AC}$.

A boat moves from $P_1(0.5, 1.2)$ to $P_2(2.3, 3.8)$ (in km). Find the displacement vector.

Determine the vector $\overrightarrow{BA}$ for $A(-1,4)$ and $B(3,-2)$.

Calculate the magnitude of the vector from $P(0,0)$ to $Q(4,3)$.

Given $A(2,-1)$, $B(5,3)$, $C(-1,4)$ and $D(2,0)$, find $\overrightarrow{AB}$ and $\overrightarrow{CD}$, then determine whether they are parallel.

Find the vector $\overrightarrow{AB}$ given $A(2,3)$ and $B(5,7)$.

Find the value of $k$ such that the vector from $A(1,1)$ to $B(k,3)$ is perpendicular to $\begin{pmatrix} 2 \\ -1 \end{pmatrix}$.

Given $A(-2,5)$ and $B(3,1)$, first find the midpoint $M$, then find $\overrightarrow{AM}$.

Calculate the vector $\overrightarrow{AB}$ for $A\left(\frac{1}{2},-\frac{3}{4}\right)$ and $B\left(\frac{5}{2},\frac{1}{4}\right)$.

Find the unit vector in the direction from $A(1,2)$ to $B(4,6)$.