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Find the following for the vectors u = - 5 i+4j + v7 k and v = 5 i - 4 j- V7 k. a. v•u, lv], and Ju| b. the cosine of the angle between v and u c. the scalar projection of u in the direction of v d. the vector projection of u in the direction of v v•u= (Simplify your answer.) |v| =D (Simplify your answer. Type an exact answer, using radicals as needed or round to the nearest thousandth.) lu|=D (Simplify your answer. Type an exact answer, using radicals as needed or round to the nearest thousandth.) The cosine of the angle between v and u is (Simplify your answer. Type an exact answer, using radicals as needed or round to the nearest thousandth. Do not rationalize the c The scalar projection of u in the direction of v is. (Simplify your answer. Type an exact answer, using radicals as needed or round to the nearest thousandth. Rationalize the denomi The vector projection of u in the direction of v is + () K uy = i+ (Simplify your answers. Type exact answers, using radicals as needed or round to the nearest thousandth.)

Find the following for the vectors u = - 5 i+4j + v7 k and v = 5 i - 4 j- V7 k. a. v•u, lv], and Ju| b. the cosine of the angle between v and u c. the scalar projection of u in the direction of v d. the vector projection of u in the direction of v v•u= (Simplify your answer.) |v| =D (Simplify your answer. Type an exact answer, using radicals as needed or round to the nearest thousandth.) lu|=D (Simplify your answer. Type an exact answer, using radicals as needed or round to the nearest thousandth.) The cosine of the angle between v and u is (Simplify your answer. Type an exact answer, using radicals as needed or round to the nearest thousandth. Do not rationalize the c The scalar projection of u in the direction of v is. (Simplify your answer. Type an exact answer, using radicals as needed or round to the nearest thousandth. Rationalize the denomi The vector projection of u in the direction of v is + () K uy = i+ (Simplify your answers. Type exact answers, using radicals as needed or round to the nearest thousandth.)

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter8: Applications Of Trigonometry
Section8.4: The Dot Product
Problem 31E
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Find the following for the vectors u = - 5 i+4j + V7 k and v= 5 i-4 j- V7 k. a. v•u, v, and u b. the cosine of the angle between v and u c. the scalar projection of u in the direction of v d. the vector projection of u in the direction of v v•u = (Simplify your answer.) |v| (Simplify your answer. Type an exact answer, using radicals as needed or round to the nearest thousandth.) |u| = (Simplify your answer. Type an exact answer, using radicals as needed or round to the nearest thousandth.) The cosine of the angle between v and u is. (Simplify your answer. Type an exact answer, using radicals as needed or round to the nearest thousandth. Do not rationalize the denominator.) The scalar projection of u in the direction of v is (Simplify your answer. Type an exact answer, using radicals as needed or round to the nearest thousandth. Rationalize the denominator.) The vector projection of u in the direction of v is u, = (O i+ (O i+ (O k (Simplify your answers. Type exact answers, using radicals as needed or round to the nearest thousandth.)
Transcribed Image Text:Find the following for the vectors u = - 5 i+4j + V7 k and v= 5 i-4 j- V7 k. a. v•u, v, and u b. the cosine of the angle between v and u c. the scalar projection of u in the direction of v d. the vector projection of u in the direction of v v•u = (Simplify your answer.) |v| (Simplify your answer. Type an exact answer, using radicals as needed or round to the nearest thousandth.) |u| = (Simplify your answer. Type an exact answer, using radicals as needed or round to the nearest thousandth.) The cosine of the angle between v and u is. (Simplify your answer. Type an exact answer, using radicals as needed or round to the nearest thousandth. Do not rationalize the denominator.) The scalar projection of u in the direction of v is (Simplify your answer. Type an exact answer, using radicals as needed or round to the nearest thousandth. Rationalize the denominator.) The vector projection of u in the direction of v is u, = (O i+ (O i+ (O k (Simplify your answers. Type exact answers, using radicals as needed or round to the nearest thousandth.)
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