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?

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

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

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?

If you draw all possible diagonals from a single vertex of a regular $decagon$, how many distinct triangles can be formed using that vertex and two other vertices of the $decagon$?

Given the line with parametric equations $x=1+2t$, $y=3-t$, $z=4+5t$, find the perpendicular distance from the point $(2,1,0)$ to the line.

Given the vector $4i-j+8k$, which of the following is a unit vector in the same direction?

Given the vectors $a=\left(3,,,12\right)$ and $b=\left(6,,,9\right)$, find the orthogonal projection of $a$ onto $b$ (denoted as $\mathrm{orth}ab$).

Refer to vectors a through h below. Make a copy or a sketch of each vector, and then draw a sketch to represent each of the following. For example, find a + e by placing a and e so that their initial points coincide. Then use the parallelogram rule to find the resultant, as shown in the figure on the right.

<IMAGE>

a + (b + c)