Given the vectors v and u, answer a. through d. below. v= 7i-3k u=i+j+k a. Find the dot product of v and u. u v = Find the length of v. v = |(Type an exact answer, using radicals as needed.) Find the length of u. Ju =(Type an exact answer, using radicals as needed.) b. Find the cosine of the angle between v and u, cos 0= = |(Type an exact answer using radicals as needed.) c. Find the scalar component of u in the direction of v (Type an exact answer, using radicals as needed.) d. Find the vector projection of u onto v. proj, u= (Type your answer in terms of i, j, and k.)

Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
Question
Given the vectors v and u, answer a. through d. below.
v = 7i - 3k
u=i+j+k
a. Find the dot product of v and u.
=A.n
Find the length of v
|v =|(Type an exact answer, using radicals as needed.)
Find the length of u.
Ju = (Type an exact answer, using radicals as needed.).
b. Find the cosine of the angle between v and u,
cos 0=(Type an exact answer, using radicals as needed.)
c. Find the scalar component of u in the direction of v
(Type an exact answer, using radicals as needed.)
d. Find the vector projection of u onto v.
proj, u=(Type your answer in terms of i, j, and k.)
Transcribed Image Text:Given the vectors v and u, answer a. through d. below. v = 7i - 3k u=i+j+k a. Find the dot product of v and u. =A.n Find the length of v |v =|(Type an exact answer, using radicals as needed.) Find the length of u. Ju = (Type an exact answer, using radicals as needed.). b. Find the cosine of the angle between v and u, cos 0=(Type an exact answer, using radicals as needed.) c. Find the scalar component of u in the direction of v (Type an exact answer, using radicals as needed.) d. Find the vector projection of u onto v. proj, u=(Type your answer in terms of i, j, and k.)
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