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C4 vector question - I know I'm being an idiot... watch

    • Thread Starter
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    ...but I just can't figure out what the actual method is.

    The question is:

    a = 5i + 4j
    b = 2i + 3j

    Find a.b

    I know that:

    a.b = |a||b|cosx

    So what I tried was drawing out vectors a and b, working out the distance between the end of the point to make a triangle, and then using the cosine rule to work out a value for cosx.

    The answer is 22, but I get 36. I've done the qusetion twice in this way and get 36 -so can someone show me how to do this?

    Cheers.
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    There's another expression for the dot product of two vectors. Namely, \begin{pmatrix} a_1 \\ a_2 \end{pmatrix} \cdot \begin{pmatrix} b_1 \\ b_2 \end{pmatrix} = a_1b_1 + a_2b_2. You're making a lot of extra work for yourself if you try and find the angle geometrically (unless it's really obvious what the angle is; but it's not here).
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    (Original post by TenaciousMonkey)
    ...but I just can't figure out what the actual method is.

    The question is:

    a = 5i + 4j
    b = 2i + 3j

    Find a.b

    I know that:

    a.b = |a||b|cosx

    So what I tried was drawing out vectors a and b, working out the distance between the end of the point to make a triangle, and then using the cosine rule to work out a value for cosx.

    The answer is 22, but I get 36. I've done the qusetion twice in this way and get 36 -so can someone show me how to do this?

    Cheers.
    use Cosx = (a.b)/(|a|x|b|)

    so in your case it would be...

    (5x2) + (4x3) = 22

    then do 22 divided by...

    |a| x |b|

    this gives you cosx.. do cos^-1 of your answer to get x
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    (Original post by cor_fortis)
    use Cosx = (a.b)/(|a|x|b|)

    so in your case it would be...

    (5x2) + (4x3) = 22

    then do 22 divided by...

    |a| x |b|

    this gives you cosx.. do cos^-1 of your answer to get x
    The OP was trying to find a.b, not the angle (trying to find the angle was their roundabout way of finding a.b).
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    (Original post by nuodai)
    The OP was trying to find a.b, not the angle (trying to find the angle was their roundabout way of finding a.b).
    i just told him the a.b method. i'm pretty sure he's smart enough to realise which section he needs.
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    Multiply rows and add !
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    (Original post by cor_fortis)
    i just told him the a.b method. i'm pretty sure he's smart enough to realise which section he needs.
    No.

    I don't think OP knows the "direct" way of finding the dot product of two vectors like nuodai just mentioned.
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    (Original post by soutioirsim)
    No.

    I don't think OP knows the "direct" way of finding the dot product of two vectors like nuodai just mentioned.
    Bit harsh on the OP
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    (Original post by cor_fortis)
    Bit harsh on the OP
    I was saying "no" to you.
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    Nuodai has it correct, you're kind of complicating it OP!
    • Thread Starter
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    Thanks to everyone for replying.

    Like I said... I was being pretty dumb, there. My intelligence is definitely questionable

    Thanks for helping!
 
 
 
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