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# P3 vectors . watch

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1. P3 vectors .

Referred to the origin O , the points A and B have position vectors (4i-11j+4k) and (7i+j+7k) respecitvely .

a) Find a vector equation for the line passing through A and B in terms of a parameter t.
b) Find the postition vector of the point P on AB such that OP is perpendicular to AB.

I've found the vector equation of line AB ( 4i-11j+4k + t(3i + 12j + 3k) ... i've no idea how to do part b and similiar other vector questions .... help
2. First, rewrite the equation of line AB:
r = (4, -11, 4) + t(3, 12, 3) = (4, -11, 4) + t(1, 4, 1) = (4+t, 4t-11, 4+t)

AB = OB - OA = (7, 1, 7) - (4, -11, 4) = (3, 12, 3)
OP = (4+t, 4t-11, 4+t), since P lies on the line AB.

AB . OP = 0, since they're perpendicular.
(3, 12, 3) . (4+t, 4t-11, 4+t) = 0
12 + 3t + 48t - 132 + 12 + 3t = 0
=> t = 2

So:
OP = (4+2, 8-11, 4+2) = (6, -3, 6)
3. Thanks a lot ... hopefully i'll be able to solve the other questions now :-)

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