Question

find the equation of plane passing through (2,3,4) and perpendicular to x-axis

Answer 1

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 : (1, 0, 0)

The other is found by using the two points A (2, 1, -1) and B (3, 2, 1). This gives the vector AB = (1, 1, 2)

I did the vector product between (1, 0, 0) and (1, 1, 2) and obtained (0, -2, 1)

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 -1 on both sides?or is there a mistake in my calculations

Think about what a planar equation means. If

−2y+z=−3−2y+z=−3

then can we show that

2y−z=32y−z=3

(and vice versa) to show that they're equivalent?