One technique for measuring the angle of a prism is A parallel beam of light is directed onto the apex of the prism so that the beam reflects from opposite faces of the prism. Show that the angular separation of the two reflected beams is given by B 5 2A.

Use the εijk notation and derive the identity (A × B) × (C × D) = (ABD)C − (ABC)D

Find the cross product for (a) and (b) and (c) and and (d) and

Calculate the result for each of the following cases using the correct number of significant figures. a. 3.07670 10.988 b. 1.0093 105 9.98 104 c. 5.44231064.008103

Review. The graph in Figure P7.20 specifies a functional relationship between the two variables u and v. (a) Find abudv. (b) Find baudv. (c) Find abvdu. Figure P7.20

For what values of a are the vectors A = 2ai − 2j + ak and B = ai + 2aj + 2k perpendicular?

(a) Calculate Earth's average speed relative to the Sun. (b) What is its average velocity over a period of one year?

Two calipers in a national park hike from their cabin to the same spot on a lake, each taking a different path, as illustrated below. The total distance traveled along Path 1 is 7.5 km, and that along Path 2 is 82 km. What is the final displacement of each camper?

(a) Determine the weight on the Moon of a person whose weight on the Earth is 180 lb. (b) What would be your weight on the Moon?

Math Review (a) Solve the equation 7.20 103 m/s = (4.20 103 m/s) ln (Mi/Mf) for the fraction Mi/Mf. (b) If Mi = 2.65 104 kg, calculate Mf.