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A = 4i - 2j+4k and B = 3i – 6j – 2k, be two non-zero vectors. Find i. A.B. ii. the angle between A and B using vector cross product.

A = 4i - 2j+4k and B = 3i – 6j – 2k, be two non-zero vectors. Find i. A.B. ii. the angle between A and B using vector cross product.

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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(a) Let à = 4i — 2j + 4k and B = 3i - 6j – 2k, be two non-zero vectors. Find i. A.B. ii. the angle between A and B using vector cross product. (b) If ¢ = 3x²y + y²z³ and F = xzi + (2x² − y)j — yz²k, find i. Vo, ii. V . F, iii. V × Ē, iv. div(oF), V. curl(OF). (c) A particle moves so that its position vector is given by r(t) = cos wti + sin wtj, where w is a constant. Show that i. the velocity of the particle is perpendicular to 7, i.e. 7. 7 = 0. ii. the acceleration à is directed towards the origin. iii. TX 7= wk, where wk is a constant vector.
Transcribed Image Text:(a) Let à = 4i — 2j + 4k and B = 3i - 6j – 2k, be two non-zero vectors. Find i. A.B. ii. the angle between A and B using vector cross product. (b) If ¢ = 3x²y + y²z³ and F = xzi + (2x² − y)j — yz²k, find i. Vo, ii. V . F, iii. V × Ē, iv. div(oF), V. curl(OF). (c) A particle moves so that its position vector is given by r(t) = cos wti + sin wtj, where w is a constant. Show that i. the velocity of the particle is perpendicular to 7, i.e. 7. 7 = 0. ii. the acceleration à is directed towards the origin. iii. TX 7= wk, where wk is a constant vector.
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