Five examples of working with equations in three dimensional space:
1. Find an equation of the plane which is parallel to the yz-plane and contains the point
P(2,4,2).
2. Find an equation (or equations) that describe the set of points in R3 which are equidistant from P (1, 2, 3) and Q(1, 0, 1).
3. Find the equations of the circle in R3 parallel to the xz-plane, centered at P(2, 9,−4)
with radius 3.
4. What set of points in R3 is described by x = −2, y = 4? Does this set intersect the
sphere x^2 + 2x + y^2 + z^2 − 6z = 90?
5. Find the perpendicular distance from P (4, 1,−2) to the xy-plane. Then find the distance from P to the z-axis.
#mathematics #math #multivariablecalculus #calculus #vectorcalculus #iitjammathematics #calculus3
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