Operations on vectors

Find the cross product u x v if

u = < 2, 0, 1 > and v = < 0, 0 , -1 >.

• 2

• < 0, 2, 0 >

• -2

• < 0, -2, 0 >

What do you need to get an equation of a plane?

• An orthogonal vector

• A normal vector to the plane

• A point on the plane

• An orthogonal vector to the plane and a point on the plane

The scalar projection of vector u=(-7,4) onto vector v=(4, -3) is

• 8

• 40

• -8

• -16

• 11𝑖-13𝑗+3𝑘

• -11𝑖+13𝑗−3𝑘

• 1𝑖+13𝑗−3𝑘

• 11𝑖+13𝑗−3𝑘

• 60°

• 75°

• 81°

• 85°

Which vectors are parallel with 2s + t?

• 2s + 2t

• 4s + 2t

• 3s + 2t

• 0.5t + s

• -2s - t

If vector u is orthogonal to vector v, then the Proj_v u =

• 1

• undefined

• infinity

• -1

• 0

Find the angle between vectors (1,3) and (2,-5).

• 40.2°

• 49.7°

• 139.7°

• 92.6°

The dot product can be used with two and three dimensional vectors

• I agree

• I disagree

• It depends

• Not sure

Are the two vectors parallel, orthogonal, or neither? a = <-5, -2> and b = <4, -10>?

• parallel

• orthogonal

• neither

• undefined