Explanation Given info: The vector A → is 3 i ^ + j ^ − k ^ , the vector B → is − i ^ + 2 j ^ + 5 k ^ and the vector C → is 2 j ^ − 3 k ^ . From the properties of dot products, the relation of unit like vectors is, i ^ ⋅ i ^ = j ^ ⋅ j ^ = k ^ ⋅ k ^ = 1 From the properties of dot products, the relation of unit unlike vectors is, i ^ ⋅ j ^ = j ^ ⋅ k ^ = k ^ ⋅ i ^ = 0 From the distributive property of multiplication, the scalar product of vectors is, C → ⋅ ( A → − B → ) = C → ⋅ A → − C → ⋅ B → Substitute 3 i ^ + j ^ − k ^ for A → , − i ^ + 2 j ^ + 5 k ^ for B → and 2 j ^ − 3 k ^ for C → in the above equation. C → ⋅ ( A → − B → ) = ( 2 j ^ − 3 k ^ ) ⋅ ( 3 i ^ + j ^ − k ^ ) − ( 2 j ^ − 3 k ^ ) ⋅ ( − i ^ + 2 j ^ + 5 k ^ ) = [ ( 2 j ^ ) ⋅ ( 3 i ^ ) + ( 2 j ^ ) ⋅ ( j ^ ) + ( 2 j ^ ) ⋅ ( − k ^ ) − ( 3 k ^ ) ⋅ ( 3 i ^ ) − ( 3 k ^ ) ⋅ ( j ^ ) − ( 3 k ^ ) ⋅ ( − k ^ ) − ( 2 j ^ ) ⋅ ( − i ^ ) − ( 2 j ^ ) ⋅ ( 2 j ^ ) − ( 2 j ^ ) ⋅ ( 5 k ^ ) −

Physics for Scientists and Engineers, Technology Update (No access codes included)

9th Edition

ISBN: 9781305116399

Author: Raymond A. Serway, John W. Jewett

Publisher: Cengage Learning

See similar textbooks

Videos

Question

Chapter 7, Problem 7.9P

To determine

The value of the expression C→⋅(A→−B→) .

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 7, Problem 7.8P

Chapter 7, Problem 7.10P

Students have asked these similar questions

No chatgpt pls will upvote

13.87 ... Interplanetary Navigation. The most efficient way to send a spacecraft from the earth to another planet is by using a Hohmann transfer orbit (Fig. P13.87). If the orbits of the departure and destination planets are circular, the Hohmann transfer orbit is an elliptical orbit whose perihelion and aphelion are tangent to the orbits of the two planets. The rockets are fired briefly at the depar- ture planet to put the spacecraft into the transfer orbit; the spacecraft then coasts until it reaches the destination planet. The rockets are then fired again to put the spacecraft into the same orbit about the sun as the destination planet. (a) For a flight from earth to Mars, in what direction must the rockets be fired at the earth and at Mars: in the direction of motion, or opposite the direction of motion? What about for a flight from Mars to the earth? (b) How long does a one- way trip from the the earth to Mars take, between the firings of the rockets? (c) To reach Mars from the…

No chatgpt pls will upvote

Chapter 7 Solutions

Physics for Scientists and Engineers, Technology Update (No access codes included)

Ch. 7 - Prob. 7.1QQ Ch. 7 - Figure 7.4 shows four situations in which a force...Ch. 7 - Which of the following statements is true about...Ch. 7 - A dart is inserted into a spring-loaded dart gun...Ch. 7 - A dart is inserted into a spring-loaded dart gun...Ch. 7 - Choose the correct answer. The gravitational...Ch. 7 - A ball is connected to a light spring suspended...Ch. 7 - What does the slope of a graph of U(x) versus x...Ch. 7 - Alex and John are loading identical cabinets onto...Ch. 7 - If the net work done by external forces on a...

Ch. 7 - A worker pushes a wheelbarrow with a horizontal...Ch. 7 - A cart is set rolling across a level table, at the...Ch. 7 - Prob. 7.5OQ Ch. 7 - Is the work required to be done by an external...Ch. 7 - A bloc k, of mass m is dropped from the fourth...Ch. 7 - An a simple pendulum swings back and forth, the...Ch. 7 - Bullet 2 has twice the mass of bullet 1. Both are...Ch. 7 - Figure OQ7.10 shows a light extended spring...Ch. 7 - If the speed of a particle is doubled, what...Ch. 7 - Prob. 7.12OQ Ch. 7 - Prob. 7.13OQ Ch. 7 - A certain spring that obeys Hookes law is...Ch. 7 - A cart is set rolling across a level table, al the...Ch. 7 - An ice cube has been given a push and slides...Ch. 7 - Can a normal force do work? If not, why not? If...Ch. 7 - Object 1 pushes on object 2 as the objects move...Ch. 7 - A student has the idea that the total work done on...Ch. 7 - (a) For what values of the angle between two...Ch. 7 - Prob. 7.5CQ Ch. 7 - Discuss the work done by a pitcher throwing a...Ch. 7 - Prob. 7.7CQ Ch. 7 - If only one external force acts on a particle,...Ch. 7 - Prob. 7.9CQ Ch. 7 - Prob. 7.10CQ Ch. 7 - A certain uniform spring has spring constant k....Ch. 7 - Prob. 7.12CQ Ch. 7 - Does the kinetic energy of an object depend on the...Ch. 7 - Cite two examples in which a force is exerted on...Ch. 7 - A shopper in a supermarket pushes a cart with a...Ch. 7 - A raindrop of mass 3.35 10-5 kg falls vertically...Ch. 7 - In 1990, Walter Arfeuille of Belgium lifted a...Ch. 7 - The record number of boat lifts, including the...Ch. 7 - A block of mass m = 2.50 kg is pushed a distance d...Ch. 7 - Spiderman, whose mass is 80.0 kg, is dangling on...Ch. 7 - Prob. 7.7P Ch. 7 - Vector A has a magnitude of 5.00 units, and vector...Ch. 7 - Prob. 7.9P Ch. 7 - Find the scalar product of the vectors in Figure...Ch. 7 - A force F = (6i 2j) N acts on a panicle that...Ch. 7 - Using the definition of the scalar product, find...Ch. 7 - Lei B = 5.00 m at 60.0. Let the vector C have the...Ch. 7 - The force acting on a panicle varies as shown in...Ch. 7 - A particle is subject to a force Fx that varies...Ch. 7 - In a control system, an accelerometer consists of...Ch. 7 - When a 4.00-kg object is hung vertically on a...Ch. 7 - Hookes law describes a certain light spring of...Ch. 7 - An archer pulls her bowstring back 0.400 m by...Ch. 7 - A light spring with spring constant 1 200 N/m is...Ch. 7 - A light spring with spring constant k1 is hung...Ch. 7 - Express the units of the force constant of a...Ch. 7 - A cafeteria tray dispenser supports a stack of...Ch. 7 - A light spring with force constant 3.85 N/m is...Ch. 7 - A small particle of mass m is pulled to the top of...Ch. 7 - The force acting on a particle is Fx = (8x 16),...Ch. 7 - When different loads hang on a spring, the spring...Ch. 7 - A 100-g bullet is fired from a rifle having a...Ch. 7 - A force F = (4xi + 3yj), where F is in newtons and...Ch. 7 - Review. The graph in Figure P7.20 specifies a...Ch. 7 - A 3.00-kg object has a velocity (6.00i - 2.00j)...Ch. 7 - Prob. 7.32P Ch. 7 - A 0.600-kg particle has a speed of 2.00 m/s at...Ch. 7 - A 4.00-kg particle is subject to a net force that...Ch. 7 - A 2 100-kg pile driver is used to drive a steel...Ch. 7 - Review. In an electron microscope, there is an...Ch. 7 - Review. You can think of the workkinetic energy...Ch. 7 - Review. A 7.80-g bullet moving at 575 m/s strikes...Ch. 7 - Review. A 5.75-kg object passes through the origin...Ch. 7 - A 1 000-kg roller coaster car is initially at the...Ch. 7 - A 0.20-kg stone is held 1.3 m above the top edge...Ch. 7 - A 400-N child is in a swing that is attached to a...Ch. 7 - A 4.00-kg particle moves from the origin to...Ch. 7 - (a) Suppose a constant force acts on an object....Ch. 7 - A force acting on a particle moving in the xy...Ch. 7 - An object moves in the xy plane 111 Figure P7.43...Ch. 7 - Prob. 7.47P Ch. 7 - Why is the following situation impossible? A...Ch. 7 - A potential energy function for a system in which...Ch. 7 - A single conservative force acting on a particle...Ch. 7 - A single conservative force acts on a 5.0-kg...Ch. 7 - For the potential energy curve shown in Figure...Ch. 7 - A right circular cone can theoretically be...Ch. 7 - The potential energy function for a system of...Ch. 7 - Prob. 7.55AP Ch. 7 - A particle moves along the xaxis from x = 12.8 m...Ch. 7 - Two identical steel balls, each of diameter 25.4...Ch. 7 - When an object is displaced by an amount x from...Ch. 7 - A 6 000-kg freight car rolls along rails with...Ch. 7 - Why is the following situation impossible? In a...Ch. 7 - Prob. 7.61AP Ch. 7 - The spring constant of an automotive suspension...Ch. 7 - An inclined plane of angle = 20.0 has a spring of...Ch. 7 - An inclined plane of angle has a spring of force...Ch. 7 - (a) Take U = 5 for a system with a particle at...Ch. 7 - A particle of mass m = 1.18 kg is attached between...Ch. 7 - Review. A light spring has unstressed length 15.5...

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.

The value of the expression C → ⋅ ( A → − B → ) .

Solution Summary: The author explains that the value of the expression C is 16.0. From the properties of dot products, the relation of unit like vectors is,

Videos

The value of the expression C→⋅(A→−B→) .

Want to see the full answer?

Chapter 7 Solutions