Vector math -- finding vector of 2 points?

Question

Reviewing for midterm, need some help with the following:

Given the points p0 = [1 0] and p1 = [4 6] write the implicit equation for a line in vector form (i.e. compute the appropriate v and n). Is the point p2 = [1.5 3] on the line or above or below the line?

What is the equation for a plane with the norman n = [5 3 4] going through the origin?

What is the equation for the planes with the same normal but which include the point p1 = [4 6 7]?

Can someone walk me through these problems. Any help is appreciated, thank you.

Answer 1

1. Subtract to find the vector. Convert to slope-intercept form. Calculate the intercept for the line passing through the third point, and see if it's greater than or less than the original vector's intercept.

2. ax + by + cz = 0

3. Substitute x, y, and z, and calculate the new RHS value.