Understanding Normal Vectors and Equations of Planes

What is the term used to describe a vector that is perpendicular to a plane?

• Parallel

• Skew

• Normal

• Tangent

Which letter is typically used to denote a normal vector?

• u

• n

• w

• v

How do the components of a normal vector relate to the equation of a plane?

• They are the exponents of the variables.

• They are the coefficients of the variables.

• They do not appear in the equation.

• They are the constants in the equation.

What is the equation of a plane with a normal vector (2, -1, 5) passing through the point (3, 4, 1)?

• 2x + y + 5z = 0

• 2x - y + 5z = 0

• 2x - y + 5z = 7

• 2x + y - 5z = 7

What is the equation of the XY plane?

• z = 0

• x + y = 0

• y = 0

• x = 0

Which vector is normal to the YZ plane?

• (0, 0, 1)

• (1, 1, 0)

• (1, 0, 0)

• (0, 1, 0)

How do you find a normal vector when given two vectors in a plane?

• Find the dot product of the two vectors

• Find the cross product of the two vectors

• Subtract the two vectors

• Add the two vectors

What is the normal vector obtained from the cross product of vectors (3, 1, -2) and (1, 4, 1)?

• (9, -5, 11)

• (5, 9, -11)

• (11, 9, -5)

• (9, 11, -5)

If a plane passes through the origin, what is the value of the constant term in its equation?

• Depends on the normal vector

• Cannot be determined

• 0

• 1

Given points P(2, -1, -2), Q(0, 2, 1), and R(1, 3, 3), what is the equation of the plane containing these points?

• 3x + 7y - 5z = 9

• 3x - 7y + 5z = 9

• 3x + 7y + 5z = 9

• 3x - 7y - 5z = 9