ProblemsFor problems marked . refer to page 519 for a hint, clue, or answer.L1 Vector algebra 1*Given two vectors A = (21 - 3j + 76) and B= (sî + j + 2k) find:(a) A + B: (b) A -B; (c) A B. (d) A x B.%3D12 Vector algebra 2*Given two vectors A = (3i - 23 + 5k) and B = (61 - 73 + 4k) find:(a) A: (h) B: (c) (A B.13 Cosine and sine by vector algebra"Find the cosine and the sine of the angle between A = (31 + j+ k)and B = (-2i +j+ k).14 Direction cosinesThe direction cosines of a vector are the cosines of the angles itmakes with the coordinate axes. The cosines of the angles betweenthe vector and the x, y, and z axes are usually called, in turn., a.B.and y. Prove that a +B? +y = 1, using either geometry or vectoralgebra.15 Perpendicular vectorsShow that if A - Bj = |A + BỊ, then A and B are perpendicular.16 Diagonals of a parallelogramShow that the diagonals of an equilateral parallelogram areperpendicular.17 Law of sinesProve the law of sines using the cross product. It should only takea couple of lines.

Since you have posted a question with a multiple sub parts, we will solve first three sub - parts…

Answered: LI Vector algebra 1 Given two vectors A…

LI Vector algebra 1 Given two vectors A = (2i - 3j + T6) and B = (si +j+ 2k) find: (a) A+ B: (b) A- B: (c) A B: (d) A X B.

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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Question

Problems
For problems marked . refer to page 519 for a hint, clue, or answer.
L1 Vector algebra 1*
Given two vectors A = (21 - 3j + 76) and B= (sî + j + 2k) find:
(a) A + B: (b) A -B; (c) A B. (d) A x B.
%3D
12 Vector algebra 2*
Given two vectors A = (3i - 23 + 5k) and B = (61 - 73 + 4k) find:
(a) A: (h) B: (c) (A B.
13 Cosine and sine by vector algebra"
Find the cosine and the sine of the angle between A = (31 + j+ k)
and B = (-2i +j+ k).
14 Direction cosines
The direction cosines of a vector are the cosines of the angles it
makes with the coordinate axes. The cosines of the angles between
the vector and the x, y, and z axes are usually called, in turn., a.B.
and y. Prove that a +B? +y = 1, using either geometry or vector
algebra.
15 Perpendicular vectors
Show that if A - Bj = |A + BỊ, then A and B are perpendicular.
16 Diagonals of a parallelogram
Show that the diagonals of an equilateral parallelogram are
perpendicular.
17 Law of sines
Prove the law of sines using the cross product. It should only take
a couple of lines.

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