Essential University Physics Volume 1, Loose Leaf Edition (4th Edition)
4th Edition
ISBN: 9780135264669
Author: Richard Wolfson
Publisher: PEARSON
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Textbook Question
Chapter 11, Problem 5FTD
What’s the angle between two vectors if their dot product is equal to the magnitude of their cross product?
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What relative orientation of vectors results in a minimum value of magnitude of the cross product? What relative orientation of vectors results in a dot product of zero?
AA
BB
The cross product of
and
vectors was shown by
vector. Please calculate the
A = 2i – j+ 2k
B = 3i + 4j – k
vector.
a) č = Ã×B =?
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Chapter 11 Solutions
Essential University Physics Volume 1, Loose Leaf Edition (4th Edition)
Ch. 11.1 - Youre standing on the sidewalk watching a car go...Ch. 11.2 - The figure shows four pairs of force and radius...Ch. 11.3 - The figure shows three particles with the same...Ch. 11.4 - You step onto an initially nonrotating turntable...Ch. 11.5 - You push horizontally at right angles to the shaft...Ch. 11 - Does Earths angular velocity vector point north or...Ch. 11 - Figure 11.12 shows four forces acting on a body....Ch. 11 - You stand with your right arm extended...Ch. 11 - Although it contains no parentheses, the...Ch. 11 - Whats the angle between two vectors if their dot...
Ch. 11 - Why does a tetherball move faster as it winds up...Ch. 11 - Why do helicopters have two rotors?Ch. 11 - A group of polar bears is standing around the edge...Ch. 11 - Tornadoes in the northern hemisphere rotate...Ch. 11 - Does a particle moving at constant speed in a...Ch. 11 - When you turn on a high-speed power tool such as a...Ch. 11 - Why is it easier to balance a basketball on your...Ch. 11 - A bug, initially at rest on a stationary,...Ch. 11 - If you increase the rotation rate of a precessing...Ch. 11 - A car is headed north at 70 km/h. Give the...Ch. 11 - If the car of Exercise 15 makes a 90 left turn...Ch. 11 - A wheel is spinning at 45 rpm with its axis...Ch. 11 - A wheel is spinning about a horizontal axis with...Ch. 11 - A 12-N force is applied at the point x = 3 m, y =...Ch. 11 - A force F=1.3i+2.7jN is applied at the point x =...Ch. 11 - When you hold your arm outstretched, its supported...Ch. 11 - Express the units of angular momentum (a) using...Ch. 11 - In the Olympic hammer throw, a contestant whirls a...Ch. 11 - A gymnast of rotational inertia 62 kg m2 is...Ch. 11 - A 640-g hoop 90 cm in diameter is rotating at 170...Ch. 11 - A 7.4-cm-diameter baseball has mass 145 g and is...Ch. 11 - A potters wheel with rotational inertia 6.40 kg ...Ch. 11 - A 3.0-m-diametcr merry-go-round with rotational...Ch. 11 - A uniform, spherical cloud of interstellar gas has...Ch. 11 - A skater has rotational inertia 4.2 kg m2 with...Ch. 11 - You slip a wrench over a bolt. Taking the origin...Ch. 11 - Vector A points 30 counterclockwise from the...Ch. 11 - A baseball player extends his arm straight up to...Ch. 11 - Prob. 34PCh. 11 - A weightlifters barbell consists of two 25-kg...Ch. 11 - Prob. 36PCh. 11 - Two identical 1800-kg cars are traveling in...Ch. 11 - The dot product of two vectors is half the...Ch. 11 - Biomechanical engineers have developed...Ch. 11 - Figure 11.15 shows the dimensions of a 880-g...Ch. 11 - As an automotive engineer, youre charged with...Ch. 11 - A turntable of radius 25 cm and rotational inertia...Ch. 11 - A 17-kg dog is standing on the edge of a...Ch. 11 - A physics student is standing on an initially...Ch. 11 - Youre choreographing your schools annual ice show....Ch. 11 - Find the angle between two vectors whose dot...Ch. 11 - A circular bird feeder 19 cm in radius has...Ch. 11 - A force F applied at the point x = 2.0 m, y = 0 m...Ch. 11 - Prob. 49PCh. 11 - Prob. 50PCh. 11 - Jumbo is back! Jumbo is the 4.8-Mg elephant from...Ch. 11 - An anemometer for measuring wind speeds consists...Ch. 11 - A turntable has rotational inertia I and is...Ch. 11 - A uniform, solid, spherical asteroid with mass 1.2...Ch. 11 - About 99.9% of the solar systems total mass lies...Ch. 11 - Youre a civil engineer for an advanced...Ch. 11 - In Fig. 11.18, the lower disk, of mass 440 g and...Ch. 11 - A massless spring with constant k is mounted on a...Ch. 11 - A solid ball of mass M and radius R is spinning...Ch. 11 - A time-dependent torque given by = a + b sin ct...Ch. 11 - Consider a rapidly spinning gyroscope whose axis...Ch. 11 - When a star like our Sun exhausts its fuel,...Ch. 11 - Pulsarsthe rapidly rotating neutron stars...Ch. 11 - Prob. 64PCh. 11 - Figure 11.22 shows a demonstration gyroscope,...Ch. 11 - Figure 11.22 shows a demonstration gyroscope,...Ch. 11 - Figure 11.22 shows a demonstration gyroscope,...Ch. 11 - Figure 11.22 shows a demonstration gyroscope,...
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- Show that when A+B=C then A2+B2+2ABcos , where is the angle between vectors A and B .arrow_forwardWhich of the following statements is true about the relationship between the dot product of two vectors and the product of the magnitudes of the vectors? (a) AB is larger than AB. (b) AB is smaller than AB. (c) AB could be larger or smaller than AB, depending on the angle between the vectors. (d) AB could be equal to AB.arrow_forwardTwo vectors live with their tail at the same point. When the angle between them is increased by 20 degrees is there is colour product has the same magnitude but changes from positive to negative. The original angle between them wasarrow_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_forwardQuestion 5 unts Given two vectors: M = -3î + 6j – 5k and N = -2î + 3j + k ... The cross product of MxN equals Choose the best answer. A -9i -7j +3k В 21i +13j +3k 9i +7j -3k 13 E No Answerarrow_forward1. Find the dot product of A and B. 2. Find the magnitude of the cross product of A and B. 3. Given with three vectors,A = 6 m, 60 deg N of E,B = -5i + 2j mC = 7 m, SFind (A · B)C - A · (B x C)arrow_forward
- Hi! I need help with finding the cross product of 2 vectors with only an i and a j but no z/k, can you please help? everywhere ive looked for help always has a z/k component and i dont know how to figure that outarrow_forwardWhich of the following are true if two vectors are equal? Select as many. I. Their magnitudes are equal II. They point in the same direction III. Their dot product is equal to the product of their magnitudes IV. Their cross product is zeroarrow_forward10arrow_forward
- 6. Consider the two vectors. 4-3-4j B = 6k a. What is the cross product AXB? b. What is the dot product A. B?arrow_forwardQuestion 5 Given two vectors: M = -3î + 6j – 5k and N = -2î + 3j + k The cross product of MxN equals Choose the best answer. A -9i -7j +3k B 21i +13j +3k 9i +7j -3k 13 E No Answerarrow_forward44. The dot product is used to determine the I. angle between two vectors. I. projection of a vector in a specified direction. II. moment of a force. I only O Il only 1&|I Ill only 45. What is a position vector? A vector represented by a line segment beginning at the origin of an orthogonal coordinate system. O A vector with its position defined in the orthogonal coordinate system. A vector whose arrow is pointing to the right in the orthogonal coordinate system. A vector whose line segment ends at the origin of the orthogonal coordinate system. 46. The scalar product is useful for: determining the weight of falling object. angle between two vectors. resultant of two vectors. O vector product of two vectors,arrow_forward
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