Simple vector problem

Einstein

"simple" vector problem

I need help on the second part of this question:

The points A and B have position vectors (4i -11j +4k) and (7i +j +7k) respectively.

a) Find vector equation of the line passing through the two points in terms of a parameter t.

My answer: r = 4i -11j +4k + t(3i +12j +k)

b) Find the position vector of the point P on AB such that OP is perpendicular to AB where O is the origin.

I have attempted this many times but I do not know how to start. Can anyone please tell me how to. Im on the level capable of understanding scalar and dot product and converting vector equations into cartesian equations so i appreciate if you can keep it as simple as this (not too complex) and understandble. Thanks. By the way the answer to b) is 6i -3j +6k

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arcnets

Re: "simple" vector problem

Originally posted by Einstein
My answer: r = 4i -11j +4k + t(3i +12j +k)
Almost correct. Should read
r = 4i -11j +4k + t(3i +12j +3k)

For b), just remember that two vectors are perpendicular (orthogonal) WRT to each other, if their scalar product is zero.

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