Question Type 3: Performing simple calculations with vectors Exercises

Find the magnitude of $v=(4,6,1)$.

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

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

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

Given $u=(1,2,3)$ and $w=(4,0,-2)$, find $3u-2w$.

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

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

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

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

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

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

Given $u=(1,2,3)$ and $w=(4,0,-2)$, find the angle $\theta$ between them.