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Department of Mathematics
School of Physical and Mathematical Sciences
Math355 - Calculus of Several Variables
Homework 5
29-April-2021
(1) Let F be a plane in R3 containing the point (3, −1, 2). If P is perpendicular to the
vector n = i − j + 2k, then find an equation for the plane.
(2) A plane F in R3 contains the points (3, −1, 2), (2, 0, 5) and (1, −2, 4). Find an
equation of the plane F.
(3) Suppose that F is a plane in R3 which passes through the point P = (2, −1, −2).
If F is parallel to the plane described by the equation 5x − 4y + z = 25, then find
an equation of the plane F.
(4) A surface in R4 is described by an equation of the form z = f (w, x, y). Find the
equation of the tangent plane to the surface at (a, b, c, f (a, b, c)).
(5) Find the distance from the point Q = (0, 0, 1) to the surface x2 + 2y 2 and specify
the point(s) on the surface which is/are closest to Q.
- - - - - - - - - - - - - - - - - - - - - - - - Good Luck - - - - - - - - - - - - - - - - - - - - - - - - - Instructor: Vincent Teyekpiti (PhD)
Instructor: Vincent Teyekpiti (PhD)
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