IB Mathematics Applications & Interpretation Question Type 3: Performing Simple Calculations with Vectors Exercises

Given $\mathbf{u}=(1,2,3)$ and $\mathbf{w}=(4,0,-2)$, find the magnitude of $3\mathbf{u}-2\mathbf{w}$.

Given points $A=(1,2,3)$ and $B=(4,6,1)$, find the vector $\overrightarrow{AB}$.

Find the unit vector in the direction of $v=(4,6,1)$.

Find the magnitude of the vector $\mathbf{v}=\left(\begin{array}{c}4\\ 6\\ 1\end{array}\right)$.

Find the magnitude and unit vector of $\mathbf{w}=(3,-4,12)$.

Given vectors $\mathbf{u}=\left(\begin{array}{c}1\\ 2\\ 3\end{array}\right)$ and $\mathbf{w}=\left(\begin{array}{c}4\\ 0\\ -2\end{array}\right)$, find the angle $\theta$ between them.

Given $\mathbf{v}=(2,-1,2)$, find a unit vector parallel to $\mathbf{v}$.

Compute $2v-(3,-1,2)$ for $v=(4,6,1)$.

Given $A=(1,2,3)$ and $B=(4,6,1)$, find the magnitude of $\overrightarrow{AB}$.

Calculate $-v+4(3,4,3)$ for $v=(4,6,1)$.

Given $\mathbf{u}=(1,2,3)$ and $\mathbf{v}=(4,6,1)$, compute the magnitude and unit vector of $2\mathbf{u}+3\mathbf{v}$.

Given $\mathbf{u}=\left(\begin{array}{c}1\\ 2\\ 3\end{array}\right)$ and $\mathbf{w}=\left(\begin{array}{c}4\\ 0\\ -2\end{array}\right)$, find $3\mathbf{u}-2\mathbf{w}$.