8. Vectors

Given two lines $a$ and $d$ that are non-coplanar, which of the following best describes their relationship?

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

3v - 4w

Given two pairs of vectors, $a$ and $b$, and $e$ and $f$, if $a\cdot b$ = $0$ and $e\cdot f$ = $0$, what can be concluded about the relationship between each pair of vectors?

In Exercises 1–4, u and v have the same direction. In each exercise: Is u = v? Explain.

Point S lies between points R and T on a straight line. If $RT$ is $10$ centimeters long and $RS$ is $4$ centimeters, what is the length of $ST$?

Determine if the following statement is true or false: Temperature is a vector. 

Determine if the following statement is true or false: Acceleration is a vector. 

Determine if the following statement is true or false: The vectors $v$ and $-v$ point in the same direction.

Given vectors $u ⃗$ and $v ⃗$, sketch the resultant vector $u ⃗+v ⃗$

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

Given vectors $u ⃗$ and $v ⃗$, sketch the resultant vector $\(\frac\)12u⃗+v⃗$.

Given vectors $u ⃗$ and $v ⃗$, sketch the resultant vector $-2u ⃗+3v ⃗$.

In Exercises 1–4, u and v have the same direction. In each exercise: Find ||u||.

In Exercises 1–4, u and v have the same direction. In each exercise: Find ||v||.

In Exercises 1–4, u and v have the same direction. In each exercise: Find ||u||.