Given the vectors v and u, answer a. through d. below. v= 10i + 2j – 11k u=7i+24j a. Find the dot product of v and u. u v= Find the length of v v = (Simplify your answer. Type an exact answer, using radicals as needed.) Find the length of u. u| = (Simplify your answer. Type an exact answer, using radicals as needed.) b. Find the cosine of the angle between v and u. cos 0 = (Simplify your answer, including any radicals. Use integers fractions for any numbers in the expression.) c. Find the scalar component of u in the direction of v. (Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression.) d. Find the vector projection of u onto v. proj, u= (Type your answer in terms of i, j, and k. Use integers or fractions for any numbers in the expression. Do not factor.)

Given the vectors v and u, answer a. through d. below. v= 10i + 2j – 11k u=7i+24j a. Find the dot product of v and u. u v= Find the length of v v = (Simplify your answer. Type an exact answer, using radicals as needed.) Find the length of u. u| = (Simplify your answer. Type an exact answer, using radicals as needed.) b. Find the cosine of the angle between v and u. cos 0 = (Simplify your answer, including any radicals. Use integers fractions for any numbers in the expression.) c. Find the scalar component of u in the direction of v. (Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression.) d. Find the vector projection of u onto v. proj, u= (Type your answer in terms of i, j, and k. Use integers or fractions for any numbers in the expression. Do not factor.)

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter7: Distance And Approximation

Section7.1: Inner Product Spaces

Problem 7AEXP

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