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100 100
200 200200
400 400
300300
400400
Dot Product Operations with Dot Products
Angle Between Two
Vectors
Parallel, Orthogonal, or
Neither
300 300 300300
200200
400400
200
100100
500 500 500500 500500
100
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Row 1, Col 1
<4,5>·<2,3>
23
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1,2
Let u=<-1,3>, v=<2,-4>, and w=<1,-2> Find (u·v)w
What is <-14,28>?
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1,3
The angle between u=<4,3> and v=<3,5>
What is 22.2°?
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1,4
Determine whether the vectors are parallel, orthogonal,
or neither.U=<2,-3>V=<6,4>
What is orthogonal?
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2,1
<2,-1>·<1,2>
What is 0?
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2,2
Let u=<-1,3>, v=<2,-4>Find u·2v
What is -28?
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2,3
The angle between u=<4,4> and v=<-2,0>
What is 135°?
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2,4
Determine whether the vectors are parallel, orthogonal,
or neither.U=<15,45>V=<-5,12>
What is neither?
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3,1
<0,3>·<4,-2>
What is -6?
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3,2
Let u=<-1,3>, v=<2,-4>, and w=<1,-2>Find (w·u)v
What is <-14,28>?
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3,3
The angle between u=2i-3j and v=i-2j
What is 7.13°?
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3,4
Determine whether the vectors are parallel, orthogonal,
or neither.U=j
V=i-2j
What is neither?
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4,1
<-1,3>·<2,-4>
What is -14 ?
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4,2
Let u=<-1,3>Find u·u
What is 10?
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4,3
The angle between u=4j and v=-3i
What is 90°?
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4,4
Determine whether the vectors are parallel, orthogonal,
or neither.U=8i+4jV=-2i-j
What is parallel?
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5,1
<2,-3>·<6,4>
What is 0?
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5,2
Let u=<-1,3>, v=<2,-4>Find 4u·v
What is -56?
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5,3
The angle between u=-8i+4j and v=-6i-3j
What is 53.13°?
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5,4
What is orthogonal?
Determine whether the vectors are parallel, orthogonal,
or neither.U=<2,-5>V=<10,4>