EBK PHYSICS FOR SCIENTISTS & ENGINEERS
5th Edition
ISBN: 9780134296074
Author: GIANCOLI
Publisher: VST
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b) Consider two vectors ä = î - 2] + 3k, and b = 3î - 2zj + 5k, where z is a scalar.
vector & such that 3ä
4b-2c = 0.
"If vectors A = 4i + 3j + 2k and B = 2i + 3j + 4k, then the dot product A.B will be equal to"
(b) A particle moves from position A to position B in the following Cartesian
coordinate system. (Not drawn to scale)
(i)
7
6
de
B
Z
X
Fig Q1b
Find the displacement vector AB.
A
(ii) Using dot product, find the angle that the displacement vector AB make
with the x axis.
Chapter 7 Solutions
EBK PHYSICS FOR SCIENTISTS & ENGINEERS
Ch. 7.1 - A box is dragged a distance d across a floor by a...Ch. 7.1 - Return to the Chapter-Opening Question, page 163,...Ch. 7.4 - (a) Make a guess: will the work needed to...Ch. 7.4 - Can kinetic energy ever be negative?Ch. 7.4 - Prob. 1EECh. 7 - In what ways is the word work as used in everyday...Ch. 7 - A woman swimming upstream is not moving with...Ch. 7 - Can a centripetal force ever do work on an object?...Ch. 7 - Why is it tiring to push hard against a solid wall...Ch. 7 - Does the scalar product of two vectors depend on...
Ch. 7 - Can a dot product ever he negative? If yes, under...Ch. 7 - Prob. 7QCh. 7 - Does the dot product of two vectors have direction...Ch. 7 - Can the normal force on an object ever do work?...Ch. 7 - You have two springs that are identical except...Ch. 7 - Prob. 11QCh. 7 - In Example 710, it was stated that the block...Ch. 7 - Does the net work done on a particle depend on the...Ch. 7 - Prob. 2MCQCh. 7 - Prob. 3MCQCh. 7 - Prob. 5MCQCh. 7 - Prob. 7MCQCh. 7 - Prob. 8MCQCh. 7 - Prob. 9MCQCh. 7 - Prob. 10MCQCh. 7 - Prob. 12MCQCh. 7 - Prob. 13MCQCh. 7 - Prob. 14MCQCh. 7 - (I) How much work is done by the gravitational...Ch. 7 - (I) How high will a 1.85-kg rock go if thrown...Ch. 7 - (I) A 75.0-kg firefighter climbs a flight of...Ch. 7 - (I) A hammerhead with a mass of 2.0 kg is allowed...Ch. 7 - Prob. 5PCh. 7 - Prob. 6PCh. 7 - Prob. 7PCh. 7 - Prob. 8PCh. 7 - (II) Estimate the work you do to mow a lawn 10 m...Ch. 7 - Prob. 10PCh. 7 - (II) A lever such as that shown in Fig. 720 can be...Ch. 7 - Prob. 12PCh. 7 - Prob. 13PCh. 7 - Prob. 14PCh. 7 - Prob. 15PCh. 7 - Prob. 16PCh. 7 - Prob. 17PCh. 7 - Prob. 18PCh. 7 - (I) For any vector V=Vxi+Vyj+Vzk show that...Ch. 7 - Prob. 20PCh. 7 - Prob. 21PCh. 7 - Prob. 22PCh. 7 - Prob. 23PCh. 7 - (II) A constant force F=(2.0i+4.0j)N acts on an...Ch. 7 - Prob. 25PCh. 7 - Prob. 26PCh. 7 - (II) Show that if two nonparallel vectors have the...Ch. 7 - Prob. 28PCh. 7 - Prob. 29PCh. 7 - Prob. 30PCh. 7 - Prob. 31PCh. 7 - Prob. 32PCh. 7 - Prob. 33PCh. 7 - Prob. 34PCh. 7 - Prob. 35PCh. 7 - Prob. 36PCh. 7 - Prob. 37PCh. 7 - (II) If the hill in Example 72 (Fig. 74) was not...Ch. 7 - (II) The net force exerted on a particle acts in...Ch. 7 - Prob. 40PCh. 7 - (II) The force on a particle, acting along the x...Ch. 7 - Prob. 42PCh. 7 - Prob. 43PCh. 7 - (II) At the top of a pole vault, and athlete...Ch. 7 - Prob. 45PCh. 7 - Prob. 46PCh. 7 - (II) If it requires 5.0 J of work to stretch a...Ch. 7 - (II) An object, moving along the circumference of...Ch. 7 - Prob. 49PCh. 7 - Prob. 50PCh. 7 - Prob. 51PCh. 7 - Prob. 52PCh. 7 - (III) A 3.0-m-long steel chain is stretched out...Ch. 7 - (I) At room temperature, an oxygen molecule, with...Ch. 7 - (I) (a) If the kinetic energy of a particle is...Ch. 7 - Prob. 56PCh. 7 - Prob. 57PCh. 7 - Prob. 58PCh. 7 - Prob. 59PCh. 7 - (II) An 85-g arrow is fired from a bow whose...Ch. 7 - (II) If the speed of a car is increased by 50%, by...Ch. 7 - Prob. 62PCh. 7 - Prob. 63PCh. 7 - Prob. 64PCh. 7 - Prob. 65PCh. 7 - (II) (a) How much work is done by the horizontal...Ch. 7 - Prob. 67PCh. 7 - Prob. 68PCh. 7 - (II) A train is moving along a track with constant...Ch. 7 - Prob. 70PCh. 7 - Prob. 71PCh. 7 - Prob. 72PCh. 7 - Prob. 73PCh. 7 - Prob. 74GPCh. 7 - Prob. 75GPCh. 7 - Prob. 76GPCh. 7 - Prob. 77GPCh. 7 - Prob. 78GPCh. 7 - A varying force is given by F = Aekx, where x is...Ch. 7 - Prob. 80GPCh. 7 - A force F=(10.0i+9.0j+12.0k)kNacts on a small...Ch. 7 - Prob. 82GPCh. 7 - Prob. 83GPCh. 7 - Prob. 84GPCh. 7 - (III) We usually neglect the mass of a spring if...Ch. 7 - Prob. 86GPCh. 7 - Prob. 87GPCh. 7 - Prob. 88GPCh. 7 - Prob. 89GPCh. 7 - Prob. 90GPCh. 7 - Prob. 91GPCh. 7 - Assume a cyclist of weight mg can exert a force on...Ch. 7 - A car passenger buckles himself in with a seat...Ch. 7 - A simple pendulum consists of a small object of...Ch. 7 - Prob. 95GPCh. 7 - A small mass m hangs at rest from a vertical rope...Ch. 7 - Prob. 97GPCh. 7 - Prob. 98GPCh. 7 - Stretchable ropes ate used to safely arrest the...Ch. 7 - Prob. 100GP
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- Show that when A+B=C then A2+B2+2ABcos , where is the angle between vectors A and B .arrow_forwardFind the scalar components of three-dimensional vectors G and H in the following figure and write the vectors in vector component form in terms of the unit vectors of the axes.arrow_forwardIf the dot product of two vectors vanishes, what can you say about their directions?arrow_forward
- d) For the vectors A=2.00 î - 4.00 ĵ - 3.00 k and B = 5.00 ĵ - 4.00 k find the vector product A X Barrow_forwardgiven the position vectors r=(3,2,1) and r=(2,4,3), (a) Find a unit vector parallel to the resultant of the vectors, r1 and r2 (b) Find the angle between the vectors, r1 and r2, using the first the scalar product and thenm confirm your result with the cross productarrow_forward(b) A particle moves from position A to position B in the following Cartesian coordinate system. (Not drawn to scale) (i) B 9 Z -6 Fig Q1b Find the displacement vector AB. 9 A (ii) Using dot product, find the angle that the displacement vector AB make with the x axis.arrow_forward
- Given M = 3 î + j- 3k and N = 5 Î – 4 ĵ – 4 k, calculate the vector product M x N. Need Heln? Read Itarrow_forward11. Given points E(2,5,1), F(-1,4,-2), and G(3,-2,4), find: (a) a unit vector directed from . E towards F; (b) the angle between Rar and RgG: (c) the length of the perimeter of triangle EFG; (d) the scalar projection of Ra on REGarrow_forwardQuèstion 21 "If vectors A = 4i + 3j + 2k and B = 2i + 3j + 4k, then the dot product A.B will be equal to" 25 15 35 20arrow_forward
- 31P. Use the definition of scalar product, a · b = ab cos 0, and the fact that a · b = a,b̟ + a,b, + a̟b, (see Exercise 30) to calculate the angle between the two vectors given by ở 3.0k and b = 2.oî + 1.0ĵ + 3.0k. ssm 3.0î + 3.0j + ilw wwwarrow_forwardGiven the points M(0.1, -0.2, -0.1), N(-0.2, 0.1, 0.3), and P(0.4, 0, 0.1), find: (a) the vector RMN; (b)the dot product RMN. RMP ; (c) the scalar projection of RMN on RMP; (d) the vector projection of RMN on RMP; (e) the angle between RMN on RMP.arrow_forwardGiven two vectors A and B. Find the angle between them if A = { 2 , 3, 4} and B = { -2 ,2 -4, }.arrow_forward
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