MATH 2050 Linear Algebra

(Section 4)
2009 Winter

Assignment 8   -   Questions

[Sections 4.2 & 4.3   Projections, Cross Product, Planes]
Due in class on 2009 March 25 (Wednesday)

  1. Find two orthogonal non-zero vectors u and v that are both orthogonal to   w = [ 3 0 4 ]T
            [20 marks]

  1. Find the Cartesian equation of the plane that passes through the point   A(1, 2, 1)   and is parallel to the vectors   [ 0 –2 1 ]T   and   [ 2 –8 4 ]T .                 [20 marks]

  1. Find the distance   r   of the point   P(5, 6, 10)     from the line   L   that passes through the points   Q(–6, 2, 7)   and   R(1, 2, 3)   and   find the coordinates of the point   N   on the line closest to   P.                 [20 marks]

  1. Find the distance   r   of the point   P(1, 1, 1)   from the plane   P   that passes through the points   A (12, 0, 12),   B (16, –3, 10),   and   C (4, 3, 15)   and   find the Cartesian equation of the plane   and   find the coordinates of the point   N   on the plane closest to   P.                 [20 marks]

  1. Show that four distinct points A, B, C, D are all on one plane if and only if                 [20 marks]
    AB dot AC cross AD = 0

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      Created 2009 03 09 and most recently modified 2009 03 15 by Dr. G.H. George