Essential University Physics: Volume 1 (3rd Edition)
3rd Edition
ISBN: 9780321993724
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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Consider two vectors à = (1, – 3,0) and B = (0 ,0,7). Let C be their cross product: Č = à ×
В.
a) Calculate the Cartesian components of C.
b) What is the angle between vectors B and C?
Consider the 3D vectors C and D defined as C = 4i + 5j - 12k and D = 12i - 8j + 2k. Which of the following vectors is the result of the cross product, C x D?
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Chapter 11 Solutions
Essential University Physics: Volume 1 (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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- For what values of a are the vectors A = 2ai − 2j + ak and B = ai + 2aj + 2k perpendicular?arrow_forwardFind the angle between vectors for (a) D=(-3.0i-4.0j)m and A=(-3.0i+4.0j)m and (b) D=(2.0i+4.0j+K)m and B=(-2.0i+3.0j+2.0K)m .arrow_forwardShow that V = yz î+xzŷ+xy ê can be written as the curl of a vector v. Determine i for which V.i = 0.arrow_forward
- → Let 2 vectors à anb b a in the plane of modules. 12=5 ²161 = 5 e 161=5 How much is the magnitude of their vectors d=a-b knowing that the angle between the two vectors is to 60°?arrow_forwardVector A has a magnitude of 4 m and lies in the xy plane directed at 45 degrees counterclockwise from the positive x axis, whereas the vector B has a magnitude of 3m and lies in the yz plane directed at 30 degrees from the positive z axic. Find the cross product A x B and the angle between the vectors.arrow_forwardTwo vectors in Cartisian coordinates have components A= (2,2,3) and B =(4,-1,7). What is the dot product of vector A with Vector B?arrow_forward
- Given the following three vectors: A=-9î+7), B = -61 -107 and vector C has a magnitude of, ||=9 and makes and angle of 0 = 297° Determine: c) Find the dot product of vectors A and B. d) Find the cross product between vectors B and C.arrow_forwarda. Prove the triple product identity Ax(B×C)= B(A·C)-C(A·B). Begin by adopting a Cartesian coordinate system. Without loss of generality, you may orient your coordinate system such that the x axis is along B, so that B = Bi. You then have the freedom to place the y axis in the plane defined by B and C. (But wait- what happens if B and C point in the same direction, so that no such plane is defined?) Very Strong Hint: I did this in class. Look in the book!arrow_forwardThe vector product of vectors A → and B → has magnitude 12.0 m2m2 and is in the +z+-direction. Vector A → has magnitude 4.0 mm and is in the −x− -direction. Vector B → has no x-component. What is the directional angle θ of vector B → in the xy-plane measured counterclockwise from the +x+ -direction?arrow_forward
- Find the x− and y− components of the vectors A~, B~ , C~ , and D~ . TakeA = 10.0, B = 7.00, C = 10.0, and D = 9.00, and take the angles of thesevectors with respect to the +x axis to be 63◦ 161.6◦, 156◦, and 307◦,respectivelyarrow_forwardThe Vector Product Two vectors lying in the xy-plane are given by the equations A = 8î + 2j and B = -3î + 3j. Find Ax B and verify that à ×B = -B x A. SOLUTION Conceptualize Given the unit-vector notations of the vectors, think about the directions the vectors point in space. Draw them on graph paper and imagine the parallelogram for these vectors. Categorize Because we use the definition of the cross product discussed in this section, we categorize this example as-Select-- problem. Write the cross product of the two vectors: AxB = î + 2j ) x î + 3j Perform the multiplication: ĀxB = 8î x (-3î) + 8î × 3j +| j x (-3î) + 2j x Use the equations for the cross product of unit vectors to evaluate the various terms: AXB = To verify that AxB = -B x A, evaluate Bx A: BxA = (-31 + Perform the multiplication: BxA = (-31) x ]î +(-3î) × 2j + 3ĵ × 8î + j x 2j Use the equations for the cross product of unit vectors evaluate the various terms: BxA = Therefore, Ax B = -B xA As an alternative method for…arrow_forwardTwo vectors in Cartesian coordinates have components A=(2,3,2) and B=(4,-1,7). What is the dot product of vector A with vector B? A•B=arrow_forward
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