Dot Products and Vector Angles

Definitions

100

A vector that has a magnitude of zero is called this

Zero Vector

200

The angle between vectors can only be calculated if the vectors are this

Nonzero

300

u · v = u sub 1 v sub 1+ u sub 2 v sub 2 is the equation for this

Dot product

400

cos θ = (u · v) / (|u| |v|) is the equation for this

Angle between vectors

500

True or false: sin θ = (u · v) / (|u| |v|) and θ = inverse sin (u · v) / (|u| |v|) are both utilized to calculate the angle between vectors

False

Dot Products

100

Find the dot product of u and v. u = <5, 3>, v = <12, 4>

72

200

Find the dot product of u and v. u = <-2, 7>, v = <-5, -8>

-46

300

Find the dot product of u and v. u = 7i, v = -2i + 5j

-14

400

Find the dot product of u and v. u = <4, 5>, v = <-3, -7>

-47

500

Find the dot product of u and v. u = -4i - 9j. v = -3i - 2j

30

More Dot Products

100

Find the dot product of u and v. u = <-5, 2>, v = <8, 13>

-14

200

Find the dot product of u and v. u = 2i - 4j, v = -8i + 7j

-44

300

Find the dot product of u and v. u = 4i - 11j, v = -3j

33

400

Find the dot product of u and v. u = <3, 4>, v = <5, 2>

23

500

Find the dot product of u and v. u = <1, -2>, v = <-4, 3>

-10

Vector Angles

100

Find the angle between the vectors. u = <-4, -3>, v = <-1, 5>

115.56°

200

Find the angle between the vectors. u = <5, 2>, v = <-6, -1>

167.66°

300

Find the angle between the vectors. u = <2, -2>, v = <-3, -3>

90°

400

Find the angle between the vectors. u = <2, 3>, v = <-3, 5>

64.65°

500

Find the angle between the vectors. 

u = 3i - 3j

v = -2i + 2 sqrt(3)j

165°

More Vector Angles

100

Find the angle between the vectors. u = -2i, v = 5j

90°

200

Find the angle between the vectors. u = <-3, 8>, v = <-1, -9>

153.10°

300

Find the angle between the vectors. u = <2, 3>, v = <-2, 5>

55.5°

400

Find the angle between the vectors. u = <2, 1>, v = <-1, -3>

135°

500

Find the angle between the vectors. u = 2i + 6j, v = -3i + 2j

74.74°