Relative to an origin O, the position vectors of the points A, B, C, and D are given by:
$\vec{OA}=(1,3,-1) \vec{OB}=(3,-1,3) \vec{OC}=(4,2,m), \vec{OD}=(-1,0,n)$
where and are constants. Find
a) The unit vector in the direction of $\vec{AB}$
b) The value of for which angle = $90^\circ$
c) The values of for which the length of $\vec{AD}$ is $7$ units
Here is what I got :
a) $\frac{2}{6}i+\frac{4}{6}j\frac{-4}{6}k$
b) For this part, I'm not sure I got m=10? can anyone confirm, please?
c) I'm not sure how to do this
Please help!
$\mathbf{Hint:}$
b) For $2$ vectors that are perpenicular to each other use $\mathbf{a\cdot b}=0$
c) Find $AD$ in terms of $n$. Can you use the distance formula to form an equation in $n$?
Edit: The distance formula for $3$ dimensions is :
$\sqrt{x^2+y^2+z^2}$