[DarrenJackson]

Stuck on this problem for my class for a bit, I'm not sure exactly how to solve it. If someone could point me in the right direction I would really appreciate it.

What I have so far

Given the points:
A = ( 3, -4, 2)
B = (-1, -3, 5)

and the vector:

n = 2i + 5j - k

Find the displacement vector of AB = (-4, 1, 3)

Calculate the dot product (scalar product) OA . N = -16

Let THETA be the angle between the vectors OA and n. THETA is greater than 90 degrees.

Now here is where I'm stuck.

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The vector OA is to be expressed as a sum OA = kn + b, where k is a scalar and b is a vector perpendicular to n. Determine the value of k in this expression.

Using your answer from the last question, calculate the vector b.
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I know the answer is staring me in the face but I'm feeling very math-illiterate.

[ebaines]

Here's a hint: given that vector b is perpendicular to vector n, their dot product must equal zero. If we let vector b = (x,y,z), then n dot b is 2x+5y-z = 0. That's one equation. You also have (3, - 4, 2) = k(2,5,-1) + (x,y,z), which gives you three more equations. Hence you now have 4 equations in 4 unknowns, which in this case aren't too difficult to solve. Post back with your answer and we'll check it for you!