Math: Scalar Equations of a Plane

Find the scalar equation of each of the following planes. State which of the planes, if any, are coincident.

a) r = (-8,-1,8) + s(-5,1,4) + t(3,2,-4)
Scalar Equation: -12x - 8y - 13z = 0

----

b) r = (-2,-2,5) + s(3,1,-1) + t(4,1,-4)
Scalar Equation: -3x + 8y - z + 15 = 0

============

*****How do you determine if the planes are the same?

  1. 👍
  2. 👎
  3. 👁
  1. (-5,1,4) and (3,2,-4) are two direction vectors on the first plane.
    So we need a normal to these planes, the cross-product will give us that.

    Which will be (12,8,13)
    so the scalar equation will be
    12x + 8y + 13z = D
    (-8,-1,8) was given as a point on the plane, so
    12(-8) + 8(-1) + 8(13) = D
    D = 0

    so the scalar equation is
    12x + 8y + 13z = 0

    Do the second one the same way.

    1. 👍
    2. 👎

Respond to this Question

First Name

Your Response

Similar Questions

  1. Calc.

    Determine the interaction of the line of intersection of the planes x + y - z = 1 and 3x + y + z = 3 with the line of intersection of the planes 2x - y + 2z = 4 and 2x + 2y + z = 1.

  2. Calculus

    Consider the following planes. 5x − 4y + z = 1, 4x + y − 5z = 5 a) Find parametric equations for the line of intersection of the planes. b) Find the angle between the planes

  3. math

    Two planes leave simultaneously from Chicago's O'Hare Airport, one flying due north and the other due east. The northbound plane is flying 50 miles per hour faster than the eastbound plane. After 3 hours the planes are 2840 miles

  4. Geometry

    Look at the planes ABCD and EFGH shown below: Two planes ABCD and EFGH are shown. They intersect in the middle. X is the midpoint of side EF and Y is the midpoint of side DC. The two planes intersect along which of the following

  1. Calculus

    Consider the planes given by the equations 2y−2x−z=2 x−2y+3z=7 (a) Find a vector v parallel to the line of intersection of the planes. (b)Find the equation of a plane through the origin which is perpendicular to the line of

  2. Math

    1. Determine the scalar equation of the plane with vector equation Vector r= (3,-1,4) +s(2,-1,5) + t(-3,2,-2). 2. Determine the value of k so that the line with parametric equations x = 2 + 3t, y = -2 + 5t, z = kt is parallel to

  3. Calc.

    I am so confused with this last part of the unit! What in the world is going on: Use normal vectors to determine the interaction, if any, for each of the following pairs of planes. Give a geometric interpretation in each case and

  4. math

    An airline with two types of airplanes, P1 and P2, has contracted with a tour group to provide transportation for a minimum of 400 first class, 900 tourist class, and 1500 economy class passengers. For a certain trip, airplane P1

  1. physics

    Two planes of the same mass collide head-on and becomes tangled so that they move on together. If the engines of both were stopped at the moment of impact and the speeds of the planes at impact were 120m/s and 200 m/s, find the

  2. physics

    An engineer must design a runway to accommodate airplanes that must reach a ground velocity of 60 m/s before they can take off. These planes are capable of being accelerated uniformly at the rate of 2.1 m/s2. (a) How long will it

  3. Calc.

    Use normal vectors to determine the intersection, if any, for each of the following groups of three planes. Give a geometric interpretation in each case and the number of solutions for the corresponding linear system of equations.

  4. Calc.

    Use normal vectors to determine the intersection, if any, for each of the following groups of three planes. Give a geometric interpretation in each case and the number of solutions for the corresponding linear system of equations.

You can view more similar questions or ask a new question.