SOLUTION: Could anyone help on this question i asked some time back but still i haven't got no answers The position vectors of points A and B with respect to the origin O are given by

Question 471913: Could anyone help on this question i asked some time back but still i haven't got no answers
The position vectors of points A and B with respect to the origin O are given by
OA = i +3j +3k
OB = -4i + 5j +3k
Show that cos(AOB) = (4/root38)........i managed this bit
Hence or otherwise find the position vector of the point P on OB such that AP is perpendicular to OB
By putting 10^x = m show that the solution to the equation
(10^x + 10^-x)/(10^x - 10^-x) = k is x = 1/2log[(k + 1)/(k-1)]
Hence show that x = log2 + 1/2log3 - 1/2 when k = 11
Answer by richard1234(7193) (Show Source): You can put this solution on YOUR website!
I recommend you only post one problem per post. Here, you posted two problems on vectors and another completely unrelated problem. Posting several unrelated problems in one post makes it less likely that tutors will be able to provide full solutions to all of them.

For the first one, you have to find the dot product of the vectors (this should be straightforward). This is equal to |OA||OB|cos x, where |OA| denotes the magnitude of vector OA.

For the second problem, you will have to draw both vectors and point P (I can't really do this since it is three-dimensional and I will need some paper). Use the Pythagorean theorem and the scalar projections of the vectors.

For the third problem, simply replace m = 10^x. Also, you can replace 10^(-x) with 1/m. It should be recognizable as a difference of two squares, in which you can work from there.
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