8. Vectors

In Exercises 23–32, use the dot product to determine whether v and w are orthogonal.

v = 3i, w = -4i

In Exercises 1–8, use the given vectors to find v⋅w and v⋅v. v = 5i - 4j, w = -2i - j

In Exercises 40–41, use the dot product to determine whether v and w are orthogonal.

v = 12i - 8j, w = 2i + 3j

Determine whether each pair of vectors is orthogonal.

√5i - 2j, -5i + 2 √5j

Find the angle between each pair of vectors. Round to two decimal places as necessary.

3i + 4j, j

In Exercises 23–32, use the dot product to determine whether v and w are orthogonal.

v = 3i, w = -4j

In Exercises 45–50, determine whether v and w are parallel, orthogonal, or neither. v = 3i - 5j, w = 6i - 10j

Let $u$ be a unit vector, and let $v$ and $w$ be vectors, where $w$ is also a unit vector. Which of the following statements is true about the dot products $u\cdot v$ and $u\cdot w$?

Find the angle between each pair of vectors. Round to two decimal places as necessary.

〈2, 1〉, 〈-3, 1〉

If vectors $|a⃗|=3$ and $|b⃗|=7$, and $a⃗\(\cdot\) b⃗=14.85$, determine the angle between vectors $a ⃗$ and $b ⃗$.

In Exercises 23–32, use the dot product to determine whether v and w are orthogonal.

v = i + j, w = i - j

Find the angle between each pair of vectors. Round to two decimal places as necessary.

2i + 2j, -5i - 5j