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3 points lie in a plane; P1=i+2j+3k, P2=-3i+5j+2k, P3=i+2j+k. Find the Cartesian equation of the plane

Take 2 vectors on the plane, originating from the same point, that aren't parallel: P1-->P2 = P2-P1 = -4i+3j-kP1-->P3 = P3-P1 = 0i+0k-2kOne can then find the cross product of these two vectors to deter...
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Prove by mathematical induction that 11^n-6 is divisible by 5 for all natural numbers n

First I would do the base case (the first value):Test n=1,11 1 -6=5. 5 is divisible by 5 therefore true for n=1. Now we assume true for n=k,11 k -6 is divisible by 5.Next we test n=k+1,11 k+1 -6We can rearra...
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A complex number z has argument θ and modulus 1. Show that (z^n)-(z^-n)=2iSin(nθ).

This problem wants you to use De Moivre's theorem to prove a trigonometric identity.We will tackle this problem by taking the left hand side and using theorems and manipulation to show it is equivalent to th...
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Find the reflection of point P(2,4,-6) in the plane x-2y+z=6

If the point P' is a refection of point P in any plane, then both P and P' line on the line perpendicular to that plane. The equation of such line is easy to find: all we need is a point and the direction ve...
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Solve the equation 2(Sinhx)^2 -5Coshx=5, giving your answer in terms of natural logarithm in simplest form

It doesn't hurt to write down the equation again, so let's do so. Equation: 2(Sinh x ) 2 - 5Cosh x = 5 . Hmm, we don't really like to do maths with two different trig functions, why don't we see if we can re...
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