Revision history [back]

I agree with Wes about almost everything that he did. However, when I compute the cross product, I obtain the vector $\langle 2, 8, 4 \rangle$ (notice the $z$ component is $4$, not $5$. This results in the following equation for the plane:

$$2(x-4) + 8(y-0) + 4(z-0) = 0$$ $$2x - 8 + 8y + 4z = 0$$ $$2x + 8y + 4z = 8$$

We can verify that this is the correct equation by plugging in all three of our original points to make sure they satisfy this equation.

$(4, 0, 0)$: $$2(4) + 8(0) + 4(0) = 8$$ $$ 8 = 8 $$ The point $(4, 0, 0)$ works and is legit.

$(0, 1, 0)$: $$2(0) + 8(1) + 4(0) = 8$$ $$ 8 = 8 $$ The point $(0, 1, 0)$ works and is legit.

$(0, 0, 2)$: $$2(0) + 8(0) + 4(2) = 8$$ $$ 8 = 8 $$ The point $(0, 0, 2)$ works and is legit.

I agree with Wes about almost everything that he did. However, when I compute the cross product, I obtain the vector $\langle 2, 8, 4 \rangle$ (notice that the $z$ component is equal to $4$, not $5$. This results in the following equation for the plane:

$$2(x-4) + 8(y-0) + 4(z-0) = 0$$ $$2x - 8 + 8y + 4z = 0$$ $$2x + 8y + 4z = 8$$

We can verify that this is the correct equation by plugging in all three of our original points to make sure they satisfy this equation.

$(4, 0, 0)$: $$2(4) + 8(0) + 4(0) = 8$$ $$ 8 = 8 $$ The point $(4, 0, 0)$ works and is legit.

$(0, 1, 0)$: $$2(0) + 8(1) + 4(0) = 8$$ $$ 8 = 8 $$ The point $(0, 1, 0)$ works and is legit.

$(0, 0, 2)$: $$2(0) + 8(0) + 4(2) = 8$$ $$ 8 = 8 $$ The point $(0, 0, 2)$ works and is legit.

I agree with Wes about almost everything that he did. However, when I compute the cross product, I obtain the vector $\langle 2, 8, 4 \rangle$ (notice that the $z$ component is equal to $4$, not $5$. This results in the following equation for the plane:

$$2(x-4) + 8(y-0) + 4(z-0) = 0$$ $$2x - 8 + 8y + 4z = 0$$ $$2x + 8y + 4z = 8$$

We can verify that this is the correct equation by plugging in all three of our original points to make sure they satisfy this equation.

$(4, 0, 0)$: $$2(4) + 8(0) + 4(0) = 8$$ $$ 8 = 8 $$ The point $(4, 0, 0)$ works and is legit.

$(0, 1, 0)$: $$2(0) + 8(1) + 4(0) = 8$$ $$ 8 = 8 $$ The point $(0, 1, 0)$ works and is legit.

$(0, 0, 2)$: $$2(0) + 8(0) + 4(2) = 8$$ $$ 8 = 8 $$ The point $(0, 0, 2)$ works and is legit.

All three points work, so $2x + 8y + 4z = 8$ is an equation for the plane in question.