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Math Help - Finding the value of p in vectors

  1. #1
    Newbie darkfenix21's Avatar
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    Finding the value of p in vectors

    First off I hope this is in the right forum

    I've been working on two questions both of which have been giving me trouble. The first states:

    Determine "k" given two vectors and the angle between them.

    vectors a=(1,1) and b=(0,k) with and angle of 45 degrees.

    I was using the dot product to solve with with

    a.b= lal lbl cos45

    0= (sqrt 2) + kcos45

    -(sqrt 2)/cos 45 =k

    k=2

    if anyone could tell me if I'm right that be fantastic


    The second question is similar:

    Find the value of "p" if the vectors r=(p,p,1) and s+(p,-2,-3) are perpendicular to each other


    again i used the dot product and got

    0=lal lbl cos90

    0= (p)(p) +(p)(-2)+(-1)(3)

    0= (p^2) -2p -3

    3= (p^2) -2p

    this is where I get stuck so if anyone could help me out it would be much appreciated thank you
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  2. #2
    MHF Contributor
    Grandad's Avatar
    Joined
    Dec 2008
    From
    South Coast of England
    Posts
    2,570
    Hello darkfenix21
    Quote Originally Posted by darkfenix21 View Post
    First off I hope this is in the right forum

    I've been working on two questions both of which have been giving me trouble. The first states:

    Determine "k" given two vectors and the angle between them.

    vectors a=(1,1) and b=(0,k) with and angle of 45 degrees.

    I was using the dot product to solve with with

    a.b= lal lbl cos45

    0= (sqrt 2) + kcos45

    -(sqrt 2)/cos 45 =k

    k=2

    if anyone could tell me if I'm right that be fantastic
    I'm not sure what you mean here. The vectors \binom 1 1 and \binom 0 k are at 45^o for all positive values of k.


    The second question is similar:

    Find the value of "p" if the vectors r=(p,p,1) and s+(p,-2,-3) are perpendicular to each other


    again i used the dot product and got

    0=lal lbl cos90

    0= (p)(p) +(p)(-2)+(-1)(3)

    0= (p^2) -2p -3

    3= (p^2) -2p

    this is where I get stuck so if anyone could help me out it would be much appreciated thank you
    Solve the quadratic equation:
    p^2 -2p -3=0
    You can do that, can't you?

    Grandad
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  3. #3
    Newbie darkfenix21's Avatar
    Joined
    Apr 2010
    Posts
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    thank you very much for the help on the second question. That solution is so simple and i was over complicating it for myself :s kinda embarassing really.

    as for the first question I thing I arranged the equation incorrectly and k should actually be equal to .5

    as 0=lal lbl cos 45

    cos45= (sqrt2)k
    cos45/(sqrt 2)=k
    .5=k

    when subbed into the normal equation of a.b= lal lbl cos 45 as a check i get

    (1)(0)+(1)(.5)= (sqrt2)(.5)cos45

    .5=.5

    so pretty sure it was another simple and embarassing error on my part :s
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