1. Fill in the blank so that the resulting statement is true. If v and w are two nonzero vectors and 0 is the smallest nonnegative angle between them, then v . w = If v and w are two nonzero vectors and 0 is the smallest nonnegative angle between them, then v . w = (1) . (1) O |v w/ cose. O O. O aja2 + by b2. O lv| |w| sine. 2. Complete the sentence below. If v . w =0, then the two vectors v and w are If v . w =0, then the two vectors v and w are (1) _ (1) O equivalent. O parallel. O orthogonal. O congruent.3. Given v = 7i + j and w = i + 7j, find the following. a) v . w b) v . v a) v . W= b) v . V= 4. Use the given vectors to find v . w and v . v. v =7i - 2j, w = -4i -j V . WE (Simplify your answer.) V . V= (Simplify your answer.) 5. Let u = 5i -j, v = 4i + j, w = i + 3j Find the specified scalar. u . (v+ w) U . (v + W) =6. Let u = 3i -j, v = 2i + j, and w = i + 5j. Find the specified scalar. u.v+u . W u * v+U . W= (Simplify your answer.) 7. Let u = 5i -j, v = 4i + j, and w =i + 7j. Find the specified scalar. 4(u . v) 4(u . V) = (Simplify your answer.) 8. Given v = 2i -j and w = 3i + 8j, find the angle between v and w. The angle between v and w is (Do not round until the final answer. Then round to the nearest tenth as needed.)9. Find the angle between v and w. v = i + 4j, w = 4i - 3j The angle between v and w is (Do not round until the final answer. Then round to the nearest tenth as needed.) 10. Fill in each blank so that the resulting statement is true. If v = aji + bjj and w = azi + bj are vectors, the product v . w, called the , is defined as v . w = _ If v = a,i + bij and w = azi + bj are vectors, the product v . w, called the (1) is defined as V . W= (2). (1) O vector projection, (2) O b,b2. O vector components. O a,a2. O dot product, O ab1 + a2b2. O decomposition, O ajaz + by b2. 11. Let u = 5i - j, v = 5i + j, w= i + 2j Find the specified scalar. (4u) . v (4u) .V=12. Given v= - 7i + 4j and w = - 5i-j, find the angle between v and w. The angle between v and w is (Do not round until the final answer. Then round to the nearest tenth as needed.) 13. Given v = 6i - 2j and w = - i-j, a. Find projw V. b. Decompose v into two vectors v, and v2, where v, is parallel to w and v, is orthogonal to w. a. projwv = (Type your answer in terms of i and j.) b. V1 = (Type your answer in terms of i and j.) V2 = (Type your answer in terms of i and j.) 14. If v=4i + 5j and w= - 2i + 7j, find proj,v . Then decompose v into two vectors v, and v2, where v, is parallel to w and V2 is orthogonal to w. projwv = (Simplify your answer. Use integers or fractions for any numbers in the expression. Type your answer in terms of i and j.) (Simplify your answer. Use integers or fractions for any numbers in the expression. Type your answer in terms of i and j.) V2 = (Simplify your answer. Use integers or fractions for any numbers in the expression. Type your answer in terms of i and j.)15. If v = 3i + 5j and w = 6i + 10j, find proj,v . Then decompose v into two vectors v, and v2, where v, is parallel to w and v2 is orthogonal to w. projwv = (Simplify your answer. Use integers or fractions for any numbers in the expression. Type your answer in terms of i and j.) V 1 (Simplify your answer. Use integers or fractions for any numbers in the expression. Type your answer in terms of i and j.) V2 (Simplify your answer. Use integers or fractions for any numbers in the expression. Type your answer in terms of i and j.) 16. Let u = i+ j, v= 3i- 2j, and w = - 4j. Find 4u . (3v - 2w). 4u . (3v - 2w) = ( Simplify your answer.) 17. Given u = - i+ j, v = 8i -6j, and w = - 8j, find proj, (v + w). proju (v + w) = (Type your answer in terms of i and j.)18. Determine whether v and w are parallel. orthogonal, or neither. v=3i5i. w=6i 10] Choose the correct answer below. l l l parallel orthogonal L} l_l l'_,l neither 19. Find the work done in pushing a car along a level road from point A to point B, 85 feet from A. while exerting a constant force of 92 pounds. Round to the nearest foot-pound. The work dene is |:| foot-pounds. 20. A force is given by the vector F = 3i + 7]. The force moves an object along a straight line from the point (4.5} to the point (3020). Find the work done if the distance is measured in feet and the force is measured in pounds. The work done is :l (1) (Simplify your answer.) {1] C3 feet. (:3 foot-pounds. I. 3 feet per pound. {:3 pounds. :3 pounds perfoot