Unformatted text preview: 10. Find a unit vector perpendicular to the plane x + 2 y + 2 z = 10 11. Find the direction numbers of the line of intersection of the planes x + y + z = 1 and x + z = 0. 12. Find a vector equation and parametric equations for the line through the points (1, 0, 3) and (2, 1, 1). 13. Find an equation for the plane through the points (1, 2, 0), (2, 0, 1) and (5, 3, 1). 14. Find the point(s) of intersection of the line t z t y t x 4 , 1 , 1 = − = − = and the surface 2 2 2 y x z + = . 15. Show that the planes x + y – z =1 and 2 x 3 y +4 z =5 are neither parallel nor perpendicular. 16. Identify the trace of the surface 2 2 z y x + = in the plane x = 1. 17. Prove that ( a – b ) x ( a + b ) = 2( a x b) ....
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 Fall '09
 L. OLDEWURTEL
 Linear Algebra, Parametric equation

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