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anonymous

  • one year ago

precalc givin medals 1. Let u = <-4, 1>, v = <-1, 6>. Find -2u + 4v. <4, 22> <4, 7> <12, -26> <10, -14> 2. Determine whether the vectors u and v are parallel, orthogonal, or neither. u = <3, 0>, v = <0, -6> Orthogonal Neither Parallel

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  1. freckles
    • one year ago
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    u is a vector the -2 in front of the vector u is a scale factor it is just a number you multiply to each component of u

  2. freckles
    • one year ago
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    from number 2 have you considered finding the dot product?

  3. freckles
    • one year ago
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    and the magnitudes of the vectors as well

  4. freckles
    • one year ago
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    \[\cos(\theta)=\frac{a \cdot b}{|a| \cdot |b|} \\ \theta=\arccos( \frac{ a \cdot b}{|a| \cdot |b|}) \\ \text{ if } \theta=90^o \text{ then } a \text{ and } b \text{ are orthogonal } \\ \text{ but to find out if they are orthogonal you only need to see if } a \cdot b=0 \\ \text{ this is much shorter than actually finding the angle between the two vectors }\] \[\text{ if } \theta=0^o \text{ or } \theta=180^o \text{ then you have that } a \text{ and } b \\ \text{ are parallel } \\ \text{ but you don't really need to find } \theta \\ \text{ you could just see if } a \cdot b=|a| \cdot |b| \text{ or if } a \cdot b =-|a| \cdot |b|\]

  5. anonymous
    • one year ago
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    @freckles orthogonal?

  6. dan815
    • one year ago
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    u and v are definately orth as one is completely in x and the onther is in y

  7. dan815
    • one year ago
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    |dw:1435093656622:dw|

  8. dan815
    • one year ago
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    and the dot product is also 0, <3,0> dot <0,-6>=3*0+0*-6=0

  9. anonymous
    • one year ago
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    @dan815 what did u get for #1

  10. freckles
    • one year ago
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    1. Let u = <-4, 1>, v = <-1, 6>. Find -2u + 4v. do you know how to find -2u and 4v?

  11. dan815
    • one year ago
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    vector addition is done component by component

  12. anonymous
    • one year ago
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    no help @dan815 @freckles

  13. freckles
    • one year ago
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    hard to help when you don't answer questions like do you know how to find -2u and 4v? I guess you are going to just ignore that question and say we weren't helping you. I don't see how we weren't helping you unless your definition of not help is not getting a direct answer.

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