The vector $\mathbf{v}$ has initial point $P$ and terminal point $Q$. Write $\mathbf{v}$ in the form ai + bj; that is, find its position vector.
\[
P=(6,9) ; \quad Q=(4,8)
\]
What is the position vector?
$10 \mathbf{i}-17 \mathbf{j}$
$2 \mathbf{i}+\mathbf{j}$
$-2 \mathbf{i}-\mathbf{j}$
$-10 \mathbf{i}+17 \mathbf{j}$
Answer
Final Answer: \(\boxed{-2 \mathbf{i}-\mathbf{j}}\)
Step 1 ：Given points P=(6,9) and Q=(4,8).
Step 2 ：The position vector of a vector is given by the difference between the coordinates of the terminal point and the initial point.
Step 3 ：Subtract the coordinates of point P from the coordinates of point Q to get the position vector.
Step 4 ：Position vector = Q - P = (4,8) - (6,9) = (-2,-1).
Step 5 ：This corresponds to -2i - j in vector notation.
Step 6 ：Final Answer: \(\boxed{-2 \mathbf{i}-\mathbf{j}}\)
