Equations of Lines and Planes

Which of the equations below does NOT represent the line through the points A(-1,2,3) and B(2,-1,4)?

The Cartesian equation of the plane through A(-2,1,4) with vector n =3i-j+2k normal to the plane is:

• -2x + y + 4z + 1 = 0

• 3x - y + 2z + 1 = 0

• -2x + y + 4z - 1 = 0

• 3x - y + 2z - 1 = 0

• 3x + y + 8z - 29 = 0

• 3x + y + 8z + 29 = 0

• x + 2y + 3z - 29 = 0

• -2x + y  -5z + 29 = 0

The equation of the plane containing the line and the point (1,-1, 0 )

If we know the slope (m) of a line, we can write the equation for a parallel line with a point (x1, y1) using the line formula​ ​ (a)   = ​ (b)   * ​ (c)   .

• (y - y1)

• m

• (x - x1)

Find the slope of a line parallel to 6x - 2y = 8

Mathematical Equivalence

ON

Mathematical Equivalence

ON

Which equation represents the line that passes through the

points (- 7, 4) and (- 6, - 2)?

(a)  

Mathematical Equivalence

OFF

The acute angle between the planes 3y - z = 4 and

x + y - 2z = 465

is