Physics for Scientists and Engineers
6th Edition
ISBN: 9781429281843
Author: Tipler
Publisher: MAC HIGHER
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Chapter 6, Problem 44P
(a)
To determine
The x -component and y -component of two given vectors.
(b)
To determine
The scalar product of given unit vectors.
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Problem 4: It should be obvious that the magnitude of a vector is independent of the
choice of coordinate system. This implies that r r is the same for any set of axes. Use this
to prove that the dot product of two different vectors r.s is also independent of coordinate
system. [Hint: Consider the length of r + s.]
For the pair of vectors A =
(6.00î + 4.00ĵ) and B = (9.0oî – 6.00ĵ) in the xy plane, determine the following. (Enter all angle answers between 0 and 180°.)
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(a) The scalar product
A: B =
(b) The angle 0 between the vectors
(c) The angles a and ß which are respectively the (smallest) angles between the vector A and the positive x and positive y axes
a =
%D
(d) The angles y and 8, which are respectively the (smallest) angles between the vector B and the positive x and positive y axes
Y
8
%3D
For the pair of vectors A = (6.00î + 4.00j) and B = (9.00î – 6.00j) in the xy plane, determine the following. (Enter all angle answers between 0 and 180°.)
(a) The scalar product
A·B =
(b) The angle 0 between the vectors
(c) The angles a and B which are respectively the (smallest) angles between the vector A and the positive x and positive y axes
a =
B =
(d) The angles y and 8, which are respectively the (smallest) angles between the vector B and the positive x and positive y axes
8 =
Chapter 6 Solutions
Physics for Scientists and Engineers
Ch. 6 - Prob. 1PCh. 6 - Prob. 2PCh. 6 - Prob. 3PCh. 6 - Prob. 4PCh. 6 - Prob. 5PCh. 6 - Prob. 6PCh. 6 - Prob. 7PCh. 6 - Prob. 8PCh. 6 - Prob. 9PCh. 6 - Prob. 10P
Ch. 6 - Prob. 11PCh. 6 - Prob. 12PCh. 6 - Prob. 13PCh. 6 - Prob. 14PCh. 6 - Prob. 15PCh. 6 - Prob. 16PCh. 6 - Prob. 17PCh. 6 - Prob. 18PCh. 6 - Prob. 19PCh. 6 - Prob. 20PCh. 6 - Prob. 21PCh. 6 - Prob. 22PCh. 6 - Prob. 23PCh. 6 - Prob. 24PCh. 6 - Prob. 25PCh. 6 - Prob. 26PCh. 6 - Prob. 27PCh. 6 - Prob. 28PCh. 6 - Prob. 29PCh. 6 - Prob. 30PCh. 6 - Prob. 31PCh. 6 - Prob. 32PCh. 6 - Prob. 33PCh. 6 - Prob. 34PCh. 6 - Prob. 35PCh. 6 - Prob. 36PCh. 6 - Prob. 37PCh. 6 - Prob. 38PCh. 6 - Prob. 39PCh. 6 - Prob. 40PCh. 6 - Prob. 41PCh. 6 - Prob. 42PCh. 6 - Prob. 43PCh. 6 - Prob. 44PCh. 6 - Prob. 45PCh. 6 - Prob. 46PCh. 6 - Prob. 47PCh. 6 - Prob. 48PCh. 6 - Prob. 49PCh. 6 - Prob. 50PCh. 6 - Prob. 51PCh. 6 - Prob. 52PCh. 6 - Prob. 53PCh. 6 - Prob. 54PCh. 6 - Prob. 55PCh. 6 - Prob. 56PCh. 6 - Prob. 57PCh. 6 - Prob. 58PCh. 6 - Prob. 59PCh. 6 - Prob. 60PCh. 6 - Prob. 61PCh. 6 - Prob. 62PCh. 6 - Prob. 63PCh. 6 - Prob. 64PCh. 6 - Prob. 65PCh. 6 - Prob. 66PCh. 6 - Prob. 67PCh. 6 - Prob. 68PCh. 6 - Prob. 69PCh. 6 - Prob. 70PCh. 6 - Prob. 71PCh. 6 - Prob. 72PCh. 6 - Prob. 73PCh. 6 - Prob. 74P
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