# Chapter 13 - 10 Find a unit vector perpendicular to the...

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Math 4A – Castroconde Name: Worksheet 1 – Chapter 13 I.D.#: Do your work on separate sheet(s) of paper. Attach this page to your work. 1. Find an equation for the sphere having as endpoints of a diameter the points (2, 1, 4) and (4, 3, 10) 2. Let a = <-1, -4, -1>, b = <6, 2, -3>. Compute || a ||, a + 3 b , a·b , a x b , and a x ( 3 b). 3. Describe in words the region in 3 R represented by 4 2 2 + z y . 4. Find the angle between the vectors v = <2, -1, 1> and w = <3, 2, -1>. 5. Show that the quadrilateral ABCD determined by the points A (-1, 2, 0), B (3, 1, 1), C (1, 2, 1), and D (-3, 3, 0) is a parallelogram and compute its area. 6. Find the direction angles of the vector v = <1, 2, 3>. 7. Determine the value(s) of x for which the vectors <-6, x , 2> and < x , 2 x , x > are orthogonal. 8. Find the projection and component of a = <-1, -2, 2> onto b = <3, 3, 4>. 9. Determine if the points P(1, 0, 1), Q(2, 4, 6), R(3, -1, 2) and S(6, 2, 8) are coplanar.
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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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