Homework Help: Math: Scalar Equations of a Plane

Posted by Anonymous on Thursday, March 27, 2008 at 11:12pm.

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?

Math: Scalar Equations of a Plane - Reiny, Friday, March 28, 2008 at 9:15am
(-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.

Answer this Question

Related Questions

Math - Equations of planes - Write a vector equation and scalar equation of the ...
Math: Scalar Equation of a Plane - Determine whether the following pairs of ...
Math - Equation of Lines - Determine whether the following pairs of planes are ...
Maths - Properties of Planes - write a scalar equation, given it's vector ...
Math - Intersection of planes - Find the vector equation of the line of ...
Math- Intesection of a plane and line - Does the line [x,y,z]=[5,-9,3]+k[1,-12,2...
Math - intersection of planes - You are given the following two planes: x+4y-3z-...
Pre Calc - A plane (A) heading south at 120 mph and a plane (B) heading west at ...
vectors - 3 planes; $: x+2y-2z-6=0 %: 2x-y+z+8=0 £: 2x-y+2z+3=0 (a)(i)...
Vectors - 3 planes; $: x+2y-2z-6=0 %: 2x-y+z+8=0 £: 2x-y+2z+3=0 (a)(i)Find...

For Further Reading

First Name:
School Subject:
Answer: