Dot Product

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Calc IV

Last updated 9:51 PM on 4/9/26
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9 Terms

1
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Dot product of u and v

u*v=u1v1+u2v2+u3v3

<p>u*v=u<sub>1</sub>v<sub>1</sub>+u<sub>2</sub>v<sub>2</sub>+u<sub>3</sub>v<sub>3</sub></p>
2
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<p>Law of Cosine property u*v</p>

Law of Cosine property u*v

u*v=|u||v|cos(degree/theta)

<p>u*v=|u||v|cos(degree/theta)</p>
3
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Law of Cosine property cos(theta/degree)

cos(theta/degree)=u*v/(|u||v|)

<p>cos(theta/degree)=u*v/(|u||v|)</p>
4
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How do you know if 2 vectors are orthogonal?

if u*v=0

<p>if u*v=0</p>
5
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Scalar projection of u onto v

Scalvu=(u*v)/|v| (Answer should be a number)

<p>Scal<sub>v</sub>u=(u*v)/|v| (Answer should be a number)</p>
6
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Vector projection of u onto v

Projvu=(u*v)/(|v|)2*v (Answer should be in vector form ex, <u1,u2,u3>

<p>Proj<sub>v</sub>u=(u*v)/(|v|)<sup>2</sup>*v (Answer should be in vector form ex, &lt;u<sub>1</sub>,u<sub>2</sub>,u<sub>3</sub>&gt;</p>
7
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What does scalar projection tell us?

Scalar projection tells us how much of one vector lies in the direction of another

8
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What does vector projection tell us?

Vector projection tells us the component of one vector in the direction of another vector, expressed as a new vector.

<p>Vector projection tells us the component of one vector in the direction of another vector, expressed as a new vector.</p>
9
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Work done by the force F

W=F*D=|F||D|cos(theta/degree)

<p>W=F*D=|F||D|cos(theta/degree)</p>