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Page 1: 100 200 400 300 400 Dot ProductOperations with Dot Products Angle Between Two Vectors Parallel, Orthogonal, or Neither 300 200 400 200 100 500 100
Page 2: 100 200 400 300 400 Dot ProductOperations with Dot Products Angle Between Two Vectors Parallel, Orthogonal, or Neither 300 200 400 200 100 500 100

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300300

400400

Dot Product Operations with Dot Products

Angle Between Two

Vectors

Parallel, Orthogonal, or

Neither

300 300 300300

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400400

200

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500 500 500500 500500

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Page 3: 100 200 400 300 400 Dot ProductOperations with Dot Products Angle Between Two Vectors Parallel, Orthogonal, or Neither 300 200 400 200 100 500 100

Row 1, Col 1

<4,5>·<2,3>

23

Page 4: 100 200 400 300 400 Dot ProductOperations with Dot Products Angle Between Two Vectors Parallel, Orthogonal, or Neither 300 200 400 200 100 500 100

1,2

Let u=<-1,3>, v=<2,-4>, and w=<1,-2> Find (u·v)w

What is <-14,28>?

Page 5: 100 200 400 300 400 Dot ProductOperations with Dot Products Angle Between Two Vectors Parallel, Orthogonal, or Neither 300 200 400 200 100 500 100

1,3

The angle between u=<4,3> and v=<3,5>

What is 22.2°?

Page 6: 100 200 400 300 400 Dot ProductOperations with Dot Products Angle Between Two Vectors Parallel, Orthogonal, or Neither 300 200 400 200 100 500 100

1,4

Determine whether the vectors are parallel, orthogonal,

or neither.U=<2,-3>V=<6,4>

What is orthogonal?

Page 7: 100 200 400 300 400 Dot ProductOperations with Dot Products Angle Between Two Vectors Parallel, Orthogonal, or Neither 300 200 400 200 100 500 100

2,1

<2,-1>·<1,2>

What is 0?

Page 8: 100 200 400 300 400 Dot ProductOperations with Dot Products Angle Between Two Vectors Parallel, Orthogonal, or Neither 300 200 400 200 100 500 100

2,2

Let u=<-1,3>, v=<2,-4>Find u·2v

What is -28?

Page 9: 100 200 400 300 400 Dot ProductOperations with Dot Products Angle Between Two Vectors Parallel, Orthogonal, or Neither 300 200 400 200 100 500 100

2,3

The angle between u=<4,4> and v=<-2,0>

What is 135°?

Page 10: 100 200 400 300 400 Dot ProductOperations with Dot Products Angle Between Two Vectors Parallel, Orthogonal, or Neither 300 200 400 200 100 500 100

2,4

Determine whether the vectors are parallel, orthogonal,

or neither.U=<15,45>V=<-5,12>

What is neither?

Page 11: 100 200 400 300 400 Dot ProductOperations with Dot Products Angle Between Two Vectors Parallel, Orthogonal, or Neither 300 200 400 200 100 500 100

3,1

<0,3>·<4,-2>

What is -6?

Page 12: 100 200 400 300 400 Dot ProductOperations with Dot Products Angle Between Two Vectors Parallel, Orthogonal, or Neither 300 200 400 200 100 500 100

3,2

Let u=<-1,3>, v=<2,-4>, and w=<1,-2>Find (w·u)v

What is <-14,28>?

Page 13: 100 200 400 300 400 Dot ProductOperations with Dot Products Angle Between Two Vectors Parallel, Orthogonal, or Neither 300 200 400 200 100 500 100

3,3

The angle between u=2i-3j and v=i-2j

What is 7.13°?

Page 14: 100 200 400 300 400 Dot ProductOperations with Dot Products Angle Between Two Vectors Parallel, Orthogonal, or Neither 300 200 400 200 100 500 100

3,4

Determine whether the vectors are parallel, orthogonal,

or neither.U=j

V=i-2j

What is neither?

Page 15: 100 200 400 300 400 Dot ProductOperations with Dot Products Angle Between Two Vectors Parallel, Orthogonal, or Neither 300 200 400 200 100 500 100

4,1

<-1,3>·<2,-4>

What is -14 ?

Page 16: 100 200 400 300 400 Dot ProductOperations with Dot Products Angle Between Two Vectors Parallel, Orthogonal, or Neither 300 200 400 200 100 500 100

4,2

Let u=<-1,3>Find u·u

What is 10?

Page 17: 100 200 400 300 400 Dot ProductOperations with Dot Products Angle Between Two Vectors Parallel, Orthogonal, or Neither 300 200 400 200 100 500 100

4,3

The angle between u=4j and v=-3i

What is 90°?

Page 18: 100 200 400 300 400 Dot ProductOperations with Dot Products Angle Between Two Vectors Parallel, Orthogonal, or Neither 300 200 400 200 100 500 100

4,4

Determine whether the vectors are parallel, orthogonal,

or neither.U=8i+4jV=-2i-j

What is parallel?

Page 19: 100 200 400 300 400 Dot ProductOperations with Dot Products Angle Between Two Vectors Parallel, Orthogonal, or Neither 300 200 400 200 100 500 100

5,1

<2,-3>·<6,4>

What is 0?

Page 20: 100 200 400 300 400 Dot ProductOperations with Dot Products Angle Between Two Vectors Parallel, Orthogonal, or Neither 300 200 400 200 100 500 100

5,2

Let u=<-1,3>, v=<2,-4>Find 4u·v

What is -56?

Page 21: 100 200 400 300 400 Dot ProductOperations with Dot Products Angle Between Two Vectors Parallel, Orthogonal, or Neither 300 200 400 200 100 500 100

5,3

The angle between u=-8i+4j and v=-6i-3j

What is 53.13°?

Page 22: 100 200 400 300 400 Dot ProductOperations with Dot Products Angle Between Two Vectors Parallel, Orthogonal, or Neither 300 200 400 200 100 500 100

5,4

What is orthogonal?

Determine whether the vectors are parallel, orthogonal,

or neither.U=<2,-5>V=<10,4>


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