EXERCISES 12.3 EXAMPLE 8 If F in acting from P to C Wo We encounter m the work done by a v Dot Product and Projections In Exercises 1-8, find a. v. u, v, u b. the cosine of the angle between v and u c. the scalar component of u in the direction of v d. the vector proj, u. 1. v = 2i4j + √5k, u = -2i+ 4j - √5k 2. v = (3/5)i + (4/5)k, 3. v = 10i + 11j - 2k, u = 5i + 12j u = 3j + 4k 4. v = 2i+10j 11k, u = 2i + 2j + k 5. v=5j-3k, u = i +j+k 6. v = i + j, u = √2i+ √3j+ 2k 7. v = 5i + j, u = 2i + √17j 8. v = u = √2 √31 (2) Angle Between Vectors T Find the angles between the vectors in Exercises 9-12 to the hundredth of a radian. 9. u = 2i+j, v = i + 2j - k 10. u = 2i2j+k, v = 31+ 4k