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1. Show that the necessary and sufficient condition for two nonzero vectors A and B to be perpendicular is that A. B = 0.

1. Show that the necessary and sufficient condition for two nonzero vectors A and B to be perpendicular is that A. B = 0.

Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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1. Show that the necessary and sufficient condition for two nonzero vectors A and B to be perpendicular is that A. B = 0. 2. If A = 2a, + 0. 3a, – 1. 5a, and B = 10a, + 1. 5a, – 7.5a,, Show that A and B are dependent vectors. 3. Show that if A = 3a, + 2a, – a,, B = 4a, – 8a, – 4a, and C = 7ax – 6a, – 5az, then A, B and C form a right angle triangle. 4. Express the position vector r = xa, + ya, + za, in the spherical co-ordinate system. 5. (a) Obtain the length of the distance vector from point P(2, a/2, 3n/4) to Q(10, r/4, n/2) (b) Calculate the angle between the vectors A = 4ax – 2a, – az, B = ax + 4ay – 4az
Transcribed Image Text:1. Show that the necessary and sufficient condition for two nonzero vectors A and B to be perpendicular is that A. B = 0. 2. If A = 2a, + 0. 3a, – 1. 5a, and B = 10a, + 1. 5a, – 7.5a,, Show that A and B are dependent vectors. 3. Show that if A = 3a, + 2a, – a,, B = 4a, – 8a, – 4a, and C = 7ax – 6a, – 5az, then A, B and C form a right angle triangle. 4. Express the position vector r = xa, + ya, + za, in the spherical co-ordinate system. 5. (a) Obtain the length of the distance vector from point P(2, a/2, 3n/4) to Q(10, r/4, n/2) (b) Calculate the angle between the vectors A = 4ax – 2a, – az, B = ax + 4ay – 4az
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