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# 2 questions watch

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1. hi,
i need help with 2 questions.

1. find the equation of the plane that passes through

u = (1,1,5)
v = (-2,2,0)
w = (3,-1,3)

2.
find the first three terms of the taylor series for sin x around x = pi

thanks
2. 1. You need a point, and two non-parallel vectors to get the equation of the plane.

UV = v-u = -3i + j - 5k
UW = w-u = 2i - 2j - 2k = a(i - j - k) , where 'a' is some constant.

For the point, you can pick anything. Let's take (i + j + 5k), simply because it's the first one.

Eq. plane: r = (i + j + 5k) + s(-3i + j - 5k) + t(i - j - k)
3. (Original post by manps)
1. find the equation of the plane that passes through
u = (1,1,5)
v = (-2,2,0)
w = (3,-1,3)
One way is the solve the three simultaneous equations

a + b + 5c = d
-2a + 2b = d
3a - b + 3c = d

which will determine a,b,c,d up to scalar multiples

The equation of the plane is then ax+by+cz=d

Another is to find the cross product of v-u = (-3,1,-5) and w-u = (2,-2,-2) which will provide a normal vector - call it n=(n1,n2,n3)

The equation of the plane is

n1 x + n2 y + n3 z = n.u

where "." is the scalar/dot product
4. anyone got any ideas for part (b)
5. (Original post by manps)
anyone got any ideas for part (b)
taylor's theorem centred about pi says

f(x) = f(pi) + f'(pi)(x-pi) + f''(pi)/2 (x-pi)^2 + f'''(pi)/6 (x-pi)^3 +...

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