32Chapt. 3Vectors and TrigonometryFull-Answer Problems003 qfull 00350 1 3 0 easy math: prove law of sines1. The law of sines issinθaa=sinθbb=sinθcc,wherea,bandcare the sides of a general triangle andθa,θb,θcare the angles opposite thosesides. Prove the law of sines.HINT:Use trigonometry and draw an illustrative diagram.003 qfull 00510 1 3 0 easy math: adding two vectors2. You are given two vectors in component form:vectorA= (3.2,4.2)andvectorB= (−10.5,3.0).a) Give the vector sumvectorA+vectorBand vector differencevectorA−vectorBin component form.b) What is the magnitude ofvectorA+vectorB?c) What is the angle ofvectorA+vectorBrelative to the positivex-axis? The positivex-axis is the normalreference direction on the Cartesian plane.003 qfull 00640 2 3 0 moderate math: vector identity: sum and difference3. If the sum of two vectors is perpendicular to their difference, prove that the vectors have equalmagnitude.HINT:Use the dot or scalar product of sum and difference.
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