2. Suppose that vectors 35 and} in R2 are such that PI = 3, 32" = 4, and the angle between 32 and} is 71. Solve the triangle determined by the vectors 33E , 33 , and 3 3c. - 3} . That is, report all side lengths and angles in this triangle to 3 decimal places accuracy. 10. Given la |=5, | |=8 and the angle 0 = Z(a,b) =150", find: a) The magnitude of the vector a + b. A /3 b) The angle between the vector a and the vector a +b. A /2 c) The magnitude of the vector a - b. A /2 d) The magnitude of the vector 2a - 3b. A /211. If lla+bll=lla-bll. Show that a is perpendicular to b. K /33. Using the diagram below as a reference, express the vectors (TE: a}: and EB" as combinations of the vectors 3, 5 and E (that is, using sums andJ'or differences of these vectors). 1. - B r; 7 O _. A a 4. In the diagram for question 3 above, if 0 is the origin 0 (0, 0, 0), and F is the point F (3, 5, 4), and the diagram is a rectangular prism, what are the coordinates for all the other points? What are the coordinates for vector a ? What is |c3i| ? Report any approximations to three decimal places accuracy. T f4 AIS