8. Vectors

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 vectors $u ⃗$ and $v ⃗$, sketch the resultant vector $u ⃗-v ⃗$.

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?

In Exercises 21–38, let u = 2i - 5j, v = -3i + 7j, and w = -i - 6j. Find each specified vector or scalar.

v - u

Given u = 〈-2, 5〉 and v = 〈4, 3〉, find each of the following.

- 2u + 4v

A plane flies 650 mph on a bearing of 175.3°. A 25-mph wind, from a direction of 266.6°, blows against the plane. Find the resulting bearing of the plane.

Use the parallelogram rule to find the magnitude of the resultant force for the two forces shown in each figure. Round answers to the nearest tenth.

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Find the dot product for each pair of vectors.

4i, 5i - 9j

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?

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.