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Prove if it's true or false that there is a plane constructed using the dots (0,5,3), (1,-2,4) and (-1/2, 8,0).

My approximation is this:

Parameterize the equation of the plane taking (0,5,3) as the translate vector, so:

$P = (0,5,3) + r(1,-7,1) + s(-11/2, 3, 0)$

Now, given that both direction vectors r and s are non parallel then they form a basis for the 2-flat and so it is true there is a plane constructed using the dots. Is as this as simple?

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what do you mean by plane crossing between the dots? I heard about plane constructed using the dots. – Learner Mar 9 '13 at 4:05
I'm sorry, english is not my native language. I mean constructed. – Susana Mar 9 '13 at 4:06
This video might answer your question – Learner Mar 9 '13 at 4:10

Your equation for the plane will be:

$$ 18x + 2.5y - \frac{1}{2}z = 11 $$

To calculate, since eq. of plane is given as: $ax + by + cz = d $.

Let $A(0, 5, 3)$, $B(1,-2,4)$ and $C(\frac{-1}{2}, 8, 0)$. Now, find the vectors $\vec{AB}$ and $\vec{AC}$

The vector $\vec{AB}$ x $\vec{AC}$ (vector product) will give you the values for $(a, b, c)$ respectively.

To calculate $d$, satisfy the point $A$(the common vertex) in the equation.

$$ d = 0*a + 5*b + 3*c $$

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