IB Mathematics Analysis and Approaches Question Type 2: Finding a Vector Given Two Points in 3D Exercises

Find the vector from $A$ to the point dividing $\overrightarrow{AB}$ in the ratio $2:1$ (start at $A$) for $A=(1,2,3)$ and $B=(4,8,9)$.

Find the magnitude of $\overrightarrow{AB}$ for $A=(1,1,1)$ and $B=(4,5,6)$.

Find the unit vector in the direction from $B$ to $A$ for $A=(-1,0,2)$ and $B=(3,4,6)$.

Find the unit vector in the direction of $\overrightarrow{AB}$ for $A(2,3,4)$ and $B(5,7,1)$.

Find the magnitude of $\overrightarrow{AB}$ for $A=(-2,4,1)$ and $B=(3,-1,2)$.

Find a vector parallel to $\overrightarrow{AB}$ with magnitude $5$ for $A=(-3,0,2)$ and $B=(1,-4,6)$.

Find a vector of length $10$ in the direction from $A$ to $B$ for $A=(1,2,3)$ and $B=(4,8,10)$.

Find the vector $\overrightarrow{BA}$ given points $A(0,0,0)$ and $B(7,-3,5)$.

Find the magnitude of $\overrightarrow{AB}$ for $A=(1,4,2)$ and $B=(3,-2,5)$.

Find the coordinates of $P$ and the vector $\overrightarrow{AP}$.

Find the unit vector parallel to $\overrightarrow{BA}$ for $A=(2,-1,5)$ and $B=(-4,3,1)$.

Find the vector $\overrightarrow{AB}$ given $A=(2,-1,3)$ and $B=(5,2,-4)$.