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 $\mathbf{v} = \begin{pmatrix} 4 \\ 6 \\ 1 \end{pmatrix}$.

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

Given vectors $\mathbf{u} = \begin{pmatrix} 1 \\ 2 \\ 3 \end{pmatrix}$ and $\mathbf{w} = \begin{pmatrix} 4 \\ 0 \\ -2 \end{pmatrix}$, 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 $\mathbf{u}=\begin{pmatrix} 1 \\ 2 \\ 3 \end{pmatrix}$ and $\mathbf{w}=\begin{pmatrix} 4 \\ 0 \\ -2 \end{pmatrix}$, find $3\mathbf{u}-2\mathbf{w}$.