Modified Mastering Physics With Pearson Etext -- Standalone Access Card -- For Essential University Physics (3rd Edition)
3rd Edition
ISBN: 9780133857221
Author: Richard Wolfson
Publisher: PEARSON
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Chapter 11, Problem 50P
To determine
check whether the cross product of two vectors can be written as a determinant.
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Find the cross product →A × →C for
(a) A = 2.0 ^i − 4.0 ^j + ^k and C = 3.0 ^i + 4.0 ^j + 10.0 ^k
(b) A = 3.0 ^i + 4.0 ^j + 10.0 ^k and →C = 2.0 ^i − 4.0 ^j + ^k
(c) A = −3.0 ^i − 4.0 ^j and →C = −3.0 ^i + 4.0 ^j
(d ) →C = −2.0 ^i + 3.0 ^j + 2.0 ^k and A = −9.0 ^j
Answer a and b
For given vectors i=(0.8, 0.6, 0), j=(-0.6, 0.8, 0), and k=(1, 0, 0) in 3D space;find the results of the following. (i · i means the dot product between i and i, i × i means the cross product between i and i)
a) i . jb) i . kc) i x kd) i x ie) ||i × k||f) 2i → k (projection of 2i onto k)
The two vectors A⃗ =(4.7)i^+(6.9)j^+(3.7)k^A→=(4.7)i^+(6.9)j^+(3.7)k^ and B⃗ =(4.9)i^+(2.3)j^+(6.7)k^B→=(4.9)i^+(2.3)j^+(6.7)k^ define a plane containing a triangle. One vertex of this triangle contains both tails of the two vectors while the other two vertices contain each of the heads of the vectors, respectively. What is the magnitude of a vector perpendicular to this plane?
Hint: Find the cross product of the two vectors.
Chapter 11 Solutions
Modified Mastering Physics With Pearson Etext -- Standalone Access Card -- For Essential University Physics (3rd 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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