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 $1$? $t$ = $f$ =

In the context of geometric vectors, which of the following best describes orthogonal lines?

Given that segment $TQ$ is $26$ units long, what is the length of $QV$ if $TQ$ and $QV$ are collinear and $TQ$ is a part of $TV$ where $TV$ is $32$ units long?

Given the vectors $u=(3,2)$ and $v=(1,5)$, which of the following lists the correct components for $u$, $v$, $u+v$, and $u-v$ in that order?

Triangle xyz is dilated by a scale factor of $3$ centered at the origin. If the original length of side $xy$ is $5$ units, what is the length of side $xy$ after the transformation?

Which of the following pairs of $\mathrm{triangles}$ can be mapped onto each other using two reflections?

Given the points $(3,5)$ and $(-3,-5)$, which points are reflections of each other across both axes?

Which of the following is one of the basic ways to represent three-dimensional space in trigonometry?