8. Vectors

Dot Product

Open Question
Find the angle between each pair of vectors. Round to two decimal places as necessary.
2i + 2j, -5i - 5j
Open Question
Determine whether each pair of vectors is orthogonal.
〈1, 1〉, 〈1, -1〉
Open Question
Determine whether each pair of vectors is orthogonal.
√5i - 2j, -5i + 2 √5j
Open Question
Determine whether each pair of vectors is orthogonal.
i + 3√2j, 6i - √2j
Open Question
In Exercises 5–8, letv = -5i + 2j and w = 2i - 4jFind the specified vector, scalar, or angle.projᵥᵥv
Open Question
In Exercises 9–16, letu = 2i - j, v = 3i + j, and w = i + 4j.Find each specified scalar.u ⋅ (v + w)
Open Question
In Exercises 9–16, letu = 2i - j, v = 3i + j, and w = i + 4j.Find each specified scalar.u ⋅ v + u ⋅ w
Open Question
In Exercises 9–16, letu = 2i - j, v = 3i + j, and w = i + 4j.Find each specified scalar.(4u) ⋅ v
Open Question
In Exercises 9–16, letu = 2i - j, v = 3i + j, and w = i + 4j.Find each specified scalar.4(u ⋅ v)
Open Question
In Exercises 17–22, find the angle between v and w. Round to the nearest tenth of a degree.v = 2i - j, w = 3i + 4j
Open Question
In Exercises 17–22, find the angle between v and w. Round to the nearest tenth of a degree.v = -3i + 2j, w = 4i - j
Open Question
In Exercises 17–22, find the angle between v and w. Round to the nearest tenth of a degree.v = 6i, w = 5i + 4j
Open Question
In Exercises 23–32, use the dot product to determine whether v and w are orthogonal.v = i + j, w = i - j
Open Question
In Exercises 23–32, use the dot product to determine whether v and w are orthogonal.v = 2i + 8j, w = 4i - j
Open Question
In Exercises 23–32, use the dot product to determine whether v and w are orthogonal.v = 2i - 2j, w = -i + j