# A 1 0 0 b 2 0 1 and c 1 4 3 b find the area of

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Unformatted text preview: 3, u 5. For any vectors u and v in V3 and any scalar k, ku w 9. For any vectors u and v in V3, u u. 4. For any vectors u and v in V3 and any scalar k, ku v v 8. For any vectors u, v, and w in V3, v v ■ u v u. v 881 7. For any vectors u, v, and w in V3, Determine whether the statement is true or false. If it is true, explain why. If it is false, explain why or give an example that disproves the statement. 1. For any vectors u and v in V3, u v ❙❙❙❙ 11. (a) Find a vector perpendicular to the plane through the points v directed into the page or out of it? A 1, 0, 0 , B 2, 0, 1 , and C 1, 4, 3 . (b) Find the area of triangle ABC. 12. A constant force F 3 i 5 j 10 k moves an object along the line segment from 1, 0, 2 to 5, 3, 8 . Find the work done if the distance is measured in meters and the force in newtons. | v |=3 45° 13. A boat is pulled onto shore using two ropes, as shown in the | u |=2 diagram. If a force of 255 N is needed, ﬁnd the magnitude of the force in each rope. 4. Calculate the given quantity if a (a) (c) (e) (g) (i) (k) i j 2k b 3i 2j k c j 5k 2a 3b (b) b ab (d) a b (f) a b c bc (h) a cc bc ( j) proj a b comp a b The angle between a and b (correct to the nearest degree) 20° 255 N 30° 5E-13(pp 878-883) ❙❙❙❙ 882 1/18/06 11:46 AM Page 882 CHAPTER 13 VECTORS AND THE GEOMETRY OF SPACE 14. Find the magnitude of the torque about P if a 50-N force is 25. Find the distance between the planes 3x applied as shown. and 3x 26–34 50 N 30° z 31. P 15–17 |||| 1, 2 and 1, 1, 5 16. The line through 1, 0, 1 3 x 1 2 4 z y 17. The line through 2x ■ 18–20 5z y ■ ■ |||| 1 and parallel to the line 2 ■ ■ ■ ■ ■ ■ ■ t, z ■ 1 3z 4y ■ ■ 3 t, z 1 2. t, z ■ ■ 5 ■ ■ ■ ■ ■ ■ y2 ■ 16 P to the plane y 1 is twice the distance from P to the point 0, 1, 0 . Find an equation for this surface and identify it. 2 t, ■ ■ ■ ■ 4, 6 . Find the rectangular and cylindrical coordinates of the point. ■ 4 t intersects the plane 40–43 |||| Identify...
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