a. Use vectors to show that the distance from P1(x1, y1,
Chapter , Problem 12AAE(choose chapter or problem)
a. Use vectors to show that the distance from \(P_{1}\left(x_{1}, y_{1}, z_{1}\right)\) to the plane \(A x+B y+C z=D\) is
\(d=\frac{\left|A_{1}+B_{1}+C_{1}-D\right|}{\sqrt{A^{2}+B^{2}+C^{2}}}\)
b. Find an equation for the sphere that is tangent to the planes \(x+y+z=3\) and \(x+y+z=9\) if the planes \(2 x-y=0\) and \(3 x-z=0\) pass through the center of the sphere.
Equation Transcription:
Text Transcription:
P_1(x_1, y_1, z_1)
Ax + By + Cz = D
d = frac|A_1 + B_1 + C_1 -D |}{sqrt{A^2 + B^2 + C^2}
x + y + z = 3
x + y + z = 9
2x - y = 0
3x - z = 0
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