8. Vectors

Two parallel lines are crossed by a transversal. If one of the alternate interior angles is $y$ degrees and the corresponding angle on the other side of the transversal is $65$ degrees, what is the value of $y$?

Which statement is true about the relationship between points and planes in three-dimensional space?

Given that the vectors $u$, $v$, and $w$ satisfy $\left|u\right|=\left|v\right|=1$ and $u+v+w=0$, what is the magnitude of $w$?

In the context of geometric vectors, what is the term for points that lie on the same plane?

Given intersecting lines that form angles labeled $AFE$, $BFC$, $CFD$, $DFE$, and $EFA$, which pair of angles are vertical angles?

Let $MNOP$ be a square with vertices in order. If $t$ and $f$ are the magnitudes of the vectors $\overrightarrow{M}\overrightarrow{N}$ and $\overrightarrow{N}\overrightarrow{O}$ respectively, what are the values of $t$ and $f$ if the side length of the square is $1$? $t$ = $f$ =