I need to find an equation for the plane parallel to the x-axis and passing through two given points.
One vector is parallel to the $x$-axis : $\langle 1, 0, 0 \rangle$
The other is found by using the two points $A (2, 1, -1)$ and $B (3, 2, 1)$. This gives the vector $\overrightarrow{AB} = \langle 1, 1, 2 \rangle$
I calculated the vector product between $\langle 1, 0, 0 \rangle$ and $\langle 1, 1, 2 \rangle$ and obtained $\langle 0, -2, 1 \rangle$
My answer is $-2y + z = -3$ but the book gives $2y -z =3$.
My question is : can you divide the equation for a plane by $\bf{-1}$ on both sides? Or is there a mistake in my calculations?
Best Answer
Think about what a planar equation means. If
$$-2y+z=-3$$
then can we show that
$$2y-z=3$$
(and vice versa) to show that they're equivalent?