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1) Given vectors à = (1, 2, 3), b = (-3, 1, -2), and c = (1, -2,-4), find ANY FOUR of the following: a. Find: i. 4ā-26 b. Find the angle between a and 5. ii. a x b e parallel to b? Why/why not? iii. b C. Is è perpendicular to b? Find a vector perpendicular to both c and b. d. Find the vector projection of bonto ā. e. Find the area of the parallelogram defined by the vectors a and c.

1) Given vectors à = (1, 2, 3), b = (-3, 1, -2), and c = (1, -2,-4), find ANY FOUR of the following: a. Find: i. 4ā-26 b. Find the angle between a and 5. ii. a x b e parallel to b? Why/why not? iii. b C. Is è perpendicular to b? Find a vector perpendicular to both c and b. d. Find the vector projection of bonto ā. e. Find the area of the parallelogram defined by the vectors a and c.

Calculus: Early Transcendentals
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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1) Given vectors à = (1, 2, 3), b = (-3, 1, -2), and c = (1, -2,-4), find ANY FOUR of the following: a. Find: i. 4ā-26 b. Find the angle between a and 5. ii. a x b e parallel to b? Why/why not? iii. b C. Is è perpendicular to b? Find a vector perpendicular to both c and b. d. Find the vector projection of bonto ā. e. Find the area of the parallelogram defined by the vectors a and c.
Transcribed Image Text:1) Given vectors à = (1, 2, 3), b = (-3, 1, -2), and c = (1, -2,-4), find ANY FOUR of the following: a. Find: i. 4ā-26 b. Find the angle between a and 5. ii. a x b e parallel to b? Why/why not? iii. b C. Is è perpendicular to b? Find a vector perpendicular to both c and b. d. Find the vector projection of bonto ā. e. Find the area of the parallelogram defined by the vectors a and c.
Expert Solution
Step 1

Scalar multiplication of a vector is obtained by multiplying the scalar by every component of the given vector.

A vector perpendicular to both the given vectors is the cross product of the given vectors.

Two vectors are parallel if the corresponding components of both vectors are proportional.

The area of a parallelogram formed by two vectors is the magnitude of the cross-product of two given vectors.

Two vectors are perpendicular if their dot product is zero.

 

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