Vectors and Subspaces

Given u = <3, 7> and v =<-5, 4>, find 2u - 3v

• <21, 2>
• <-11, 26>
• <8, 3>
• 23

Find the magnitude of the vector <-5, 12>

• 13
• 10.91
• 7
• 17

If w = <2, -5> and y = <2, 0>, find 2w + y

• <-10, 2>

• <4, -5>

• <-6, 10>

• <6, -10>

Find the dot product of <1, -2> and <3, 2>.

• 1
• <3, -4>
• <4, 0>
• -1

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_?

• -36

• 36

• 18

• -24

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

a = < -6, -2, 8>

b = < _x_ , -12, 48 >

What is the value of _x_?

• -68

• 68

• 36

• -24

• -24

• 24

• 48

• -48

What operation you need to find an angle between two vectors?

• Dot product between the two vectors

• Dot product between the two vectors divide the magnitude of both vectors

• Cosine inverse of dot product between the two vectors divide the magnitude of both vectors

• Cross product between the two vectors

• 41

• 12

• 21

• 14

What is the angle between two orthogonal vectors?

• 180 degree

• 90 degree

• 60 degree

• 45 degree