DIRECTIONS: PREPARE MINIMUM OF 5 PROBLEMS per QUESTION

1. Find the derivative of the product between a scalar function and a vector function using the product formula.
2. Find the volume of an irregular solid using triple integration, the first integral should have at least one limit with variables.
3. Find the angle between two lines using dot product. The two lines should not pass through zero.
4. Determine the work done (line integral) in a close path using two methods. The path should contain a curve and a line. The line should not pass through (0,0). The first method should be by using directly the formula ∫ 𝐹𝐹 ∙ 𝑑𝑑𝑑𝑑 and the second method using Green’s Theorem. Give your own vector filed function F. F should be of the form <axmyn,axmyn>
5. Discuss a practical application of the cross product (vectors).