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Summary Calculus 3 task 5.docx Calculus 3 Task #5 Task #5: Vectors and Planes Plane P1 is given by the equation 2x + 5y “ 9z = 60. Plane P2 is given by the equation 4x + 2y + Cz = 0. A.Determine the value of C in the Assumptions section that makes plane P2 p$4.99
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Summary Calculus 3 task 5.docx Calculus 3 Task #5 Task #5: Vectors and Planes Plane P1 is given by the equation 2x + 5y “ 9z = 60. Plane P2 is given by the equation 4x + 2y + Cz = 0. A.Determine the value of C in the Assumptions section that makes plane P2 p
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Calculus 3 task Calculus 3 Task #5 Task #5: Vectors and Planes Plane P1 is given by the equation 2x + 5y “ 9z = 60. Plane P2 is given by the equation 4x + 2y + Cz = 0. A.Determine the value of C in the Assumptions section that makes plane P2 perpendicular to plane P1, usi...
calculus 3 task 5docx calculus 3 task 5 task 5 vectors and planes planenbspp1nbspis given by the equation 2xnbspnbsp5ynbsp“nbsp9znbspnbsp60 planenbspp2nbspis given by the
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Calculus 3 Task #5
Task #5: Vectors and Planes
Plane P1 is given by the equation 2x + 5y – 9z = 60.
Plane P2 is given by the equation 4x + 2y + Cz = 0.
A. Determine the value of C in the Assumptions section that makes plane P2 perpendicular to
plane P1, using algebra or calculus or both. Show and explain your work.
Plane P1 :2 x +5 y – 9 z=60, ⟹ the normal vector is ⃑
v 1=(2,5 ,−9)
Plane P2 :4 x +2 y+ Cz=0, ⟹ the normal vector is ⃑
v 2=(4,2 , c)
The planes are perpendicular when their normal vectors are perpendicular. So normal
vectors are perpendicular when the dot product of those vectors is equal zero.
v1∗⃑
⃑ v 2=0
(2*4) +(5*2) +(-9C) =0
8+10+(-9C) =0
18-9C=0
-9C=-18
C=-18/-9
C=2
Plugging C=2 into the dot products:
B. B. Choose three noncolinear, nonzero points on the xyz-plane. All three coordinates
of one point must be two-digit integers. The points cannot be the points given in the example
in the note below. Using the cross product, determine the equation of a plane that contains
the three chosen points. Show your work.
Point P= (1,0,2) Point Q= (2,4,6) Point R= (12,16,20)
( x 0 , y 0 , z 0 , ) is a point on plane
< a, b, c >: perpendicular to plane
v1 =⃗
⃗ PQ = < (2-1), (4-0), (6-2) > = < 1, 4, 4 >
v 2=⃗
⃗ PR = < (12-1), (16-0), (20-2) > = < 11, 16, 18 >
v1 ⋅⃗
Next, find a normal vector using the two vectors. ⃗ v 2 =⃗n
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