and spherical coordinates.- Let a = (2, 2, -1), 6= (-3, 2, 1), č = (1, 1, –4). Compute the following.%3D(a) A vector of length 13 in the direction of a.(b) The cosine of the angle between a and 6+č.(c) The volume of the parallelepiped defined by ā b, and č.(d)The vectors and such that a = 7+7 with 7 Li ond

a) The given a→=2i+2j-k Unit vector is a→a→=2i+2j-k4+4+1 =132i+2j-k Vector of length 13 in…

Answered: and spherical coordinates. - Let a =…

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...

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and spherical coordinates.
- Let a = (2, 2, -1), 6= (-3, 2, 1), č = (1, 1, –4). Compute the following.
%3D
(a) A vector of length 13 in the direction of a.
(b) The cosine of the angle between a and 6+č.
(c) The volume of the parallelepiped defined by ā b, and č.
(d)
The vectors and such that a = 7+7 with 7 Li ond

Expert Solution

Step 1

The given $\vec{a} = 2 i + 2 j - k$

Unit vector is

$\frac{\vec{a}}{|\vec{a}|} = \frac{2 i + 2 j - k}{\sqrt{4 + 4 + 1}} = \frac{1}{3} (2 i + 2 j - k)$

Vector of length 13 in the direction of $\vec{a}$

$\frac{13}{3} (2 i + 2 j - k)$

Step 2

a=<2, 2, -1>

b=<-3, 2, 1> and c=<1, 1, -4>

(b+c)=<-2, 3, -3>

$\cos θ = \frac{a . (b + c)}{|a| |b + c|} = \frac{< 2, 2, - 1 > . < - 2, 3, - 3 >}{\sqrt{4 + 4 + 1} \sqrt{4 + 9 + 9}} = \frac{- 4 + 6 + 3}{3 \sqrt{22}} = \frac{5}{3 \sqrt{22}}$

$θ = \cos^{- 1} (\frac{5}{3 \sqrt{22}}) = 69 . 2^{ο}$

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