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Set A 1. Prove using vectors that the points (4, 3, 0), (2, 0, 1), (4, 1, -1), and (2, 2, 2) are the vertices of a rectangle. 2. Let A and B be nonzero vectors. Find k E R such that A + kB is orthogonal to B – A.

Set A 1. Prove using vectors that the points (4, 3, 0), (2, 0, 1), (4, 1, -1), and (2, 2, 2) are the vertices of a rectangle. 2. Let A and B be nonzero vectors. Find k E R such that A + kB is orthogonal to B – A.

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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SEATWORK Choose a set of problems and solve all the problems in the set. Submit clear and upright photos of your solutions. Set A 1. Prove using vectors that the points (4, 3, 0), (2, 0, 1), (4, 1, -1), and (2, 2, 2) are the vertices of a rectangle. 2. Let A and B be nonzero vectors. Find k E R such that A + kB is orthogonal to B – A. Set B 1. Prove using vectors that the points (-1, 3, 3), (0, 1, 2), (2, 2, 2), and (3, 0, 1) are the vertices of a parallelogram. 2. Let Ā and B be nonzero vectors. Find k E R such that A – kB is orthogonal to A + B. Set C 1. Use vectors to find the (shortest) distance between the point (-2, 1, 4) and the line through the points (3, -2, 2) and (-2, -3, 1). 2. Let Ā and B be nonzero vectors. Find k E R such that B – kĀ is orthogonal to Ā – B.
Transcribed Image Text:SEATWORK Choose a set of problems and solve all the problems in the set. Submit clear and upright photos of your solutions. Set A 1. Prove using vectors that the points (4, 3, 0), (2, 0, 1), (4, 1, -1), and (2, 2, 2) are the vertices of a rectangle. 2. Let A and B be nonzero vectors. Find k E R such that A + kB is orthogonal to B – A. Set B 1. Prove using vectors that the points (-1, 3, 3), (0, 1, 2), (2, 2, 2), and (3, 0, 1) are the vertices of a parallelogram. 2. Let Ā and B be nonzero vectors. Find k E R such that A – kB is orthogonal to A + B. Set C 1. Use vectors to find the (shortest) distance between the point (-2, 1, 4) and the line through the points (3, -2, 2) and (-2, -3, 1). 2. Let Ā and B be nonzero vectors. Find k E R such that B – kĀ is orthogonal to Ā – B.
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