Question 1. For points A(−2,2,0), B(0,1,−1), C(−1,2,−2) find the following
(a) [3] −−→
AB ×−→
AC
(b) [2] The area of triangle ABC.
(c) [2] The equation of the plane containing A, B , and C.
2
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This is the Exam of Calculus which includes Equations, Graphs, Definition of Derivative, Constants, Squeeze Theorem, Area of Triangle etc. Key important points are: Area of Triangle, Points, Equation, Plane Containing, Property, Parametric Equations, Line of Intersection, Planes, Acute Angle, Two Planes
Typology: Exams
2012/2013
1 / 6
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Question 1. For points A(− 2 , 2 , 0), B(0, 1 , −1), C(− 1 , 2 , −2) find the following (a) [3]
AB ×
AC
(b) [2] The area of triangle ABC.
(c) [2] The equation of the plane containing A, B, and C.
2
Question 2. [4] Show the following property, a · (b × c) = (a × b) · c
Question 4. (a) [3] Plot the point whose cylindrical coordinates is (1, π/ 2 , 1). Then find its rectangular coordinates.
(b) [3] Change the point (1,
- from rectangular to spherical coordinates.
Question 5. Write the equation y^2 + z^2 = 4 using the following coordinates (a) [3] Cylindrical
(b) [3] Spherical