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c4 vectors extra watch

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    C4 - 5K question 12
    I've done a,b and c, but i'll put down the whole question as its linked (I think).
    Refered to a fixed origin O, the points A,B,C have position vecotrs (9i -2j +k), (6i +2j +6k) and (3i +pj +qk) respectively. (p/q constants)
    a. Find the equation of the line l which goes through A and B.

    b. given c is on the line, calculate p and q

    c. calculate the acute angle between OC and AB

    The point D lies on AB and is such that OD is perpendicular to AB.
    d. Find the position vector of D.


    Ok i've done a/b/c as said (after a bit of frustration and my only stupid mistakes) but now D has me stumped. Any help will be much appreciated and i'll try and will help me see where im going wrong in my working out. Cheers
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    (Original post by Daven)

    The point D lies on AB and is such that OD is perpendicular to AB.
    d. Find the position vector of D.
    From a Previous part you found the equation of l which passes through A and B. r=(9-3t)i +(4t-2)j+(1+5t)K

    We know D lies on that line so we can say D has position vector:
    OD=(9-3t)i+(4t-2)j+(1+5t)K

    To find the value of t:
    For OD and AB to perpendicular;
    OD.AB=0

    (9-3t) (-3)
    (4t-2) . (4) = 0
    (1+5t) (5)

    -3(9-3t)+4(-2+4t)+5(1+5t)=0
    -27+9t-8+16t+5+25t=0
    50t-30=0
    t=3/5

    Now sub this value for T into your point D to get exact position vector D.
    OD=(9-3(3/5))i +(4(3/5)-2)j+(1+5(3/5))k
    OD=36/5i + 2/5j +4k
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    Thanks, seems so simple :| I'll blame it on the long day
    Cheers for your work
 
 
 
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