5-4 Vectors, Dot Product, Angle, and Projection (AP Precalculus)

Fill in the blank: The dot product of vector u and vector v is -20. What is the missing x-component of v?

u = <-3, -1, 4>

v = < ??, 8, 3>

Fill in the blank: Vector a and vector b both point in the same direction.

a = < -6, -2, 8>

b = < _x_ , -12, 48 >

What is the value of _x_?

Fill in the blank: Vector a and vector b are perpendicular.

a = < -6, -2, 8>

b = < _x_ , -12, 48 >

What is the value of _x_?

Find the angle between vectors a and b. Round your answer to the nearest degree. The angle between vectors is given by cos(theta) = (a.b)/(|a||b|).

a = < 3,-7,2 >

b = < 2,2,1 >

Find the angle between the vectors. Round your answer to the nearest degree. The angle between vectors is given by cos(theta) = (a.b)/(|a||b|).

v = < -9, 6 >

w = < -1, -2 >

Calculate the angle in degrees between u=<3, 4> and v=<-4, 3>.

Calculate the angle in degrees between u=<3, 4> and v=<-6, -8>.