Explanation 1) Concept: Vector calculation can be used to find the dot product, cross product as well as addition and subtraction between two vectors. Also projection of one vector along another vector. 2) Formulae: i. i ^ j ^ k ^ p q r x y z = i ^ q z - r y - j ^ p z - r x + k ^ p y - q z w h e r e p , q , r , x , y , z a r e n u m b e r s . ii. a → . b → = ( a x b x + a y b y ) iii. a → + b → = a x + b x i ^ + ( a y + b y ) j ^ iv. C o m p o n e n t o f a → a l o n g t h e d i r e c t i o n o f b → = a → . b ^ , w h e r e b ^ = b → b → 3) Given: i. a → = 3.0 i ^ + 5.0 j ^ ii. b → = 2.0 i ^ + ( 4.0 ) j ^ 4) Calculations: Let’s take given vectors a → = 3.0 i ^ + 5.0 j ^ a n d b → = 2.0 i ^ + ( 4.0 ) j ^ a) Calculation for a → × b → i ^ j ^ k ^ 3 5 0 2 4 0 = i ^ 0 - j ^ 0 + k ^ 12 - 10 = 2 k ^ b) Calculation for a →

11th Edition

ISBN: 9781119573968

Author: David Halliday

Publisher: WILEY

See similar textbooks

Question

Chapter 3, Problem 34P

To determine

To find:

a) $a→ ×b→$

b) $a→ .b→$

c) $(a→+b→) . b→$

d) Component of $a→$ along the direction of $b→$

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 3, Problem 33P

Chapter 3, Problem 35P

Students have asked these similar questions

Two resistors of resistances R1 and R2, with R2>R1, are connected to a voltage source with voltage V0. When the resistors are connected in series, the current is Is. When the resistors are connected in parallel, the current Ip from the source is equal to 10Is. Let r be the ratio R1/R2. Find r. I know you have to find the equations for V for both situations and relate them, I'm just struggling to do so. Please explain all steps, thank you.

Bheem and Ram, jump off either side of a bridge while holding opposite ends of a rope and swing back and forth under the bridge to save a child while avoiding a fire. Looking at the swing of just Bheem, we can approximate him as a simple pendulum with a period of motion of 5.59 s. How long is the pendulum ? When Bheem swings, he goes a full distance, from side to side, of 10.2 m. What is his maximum velocity? What is his maximum acceleration?

The position of a 0.300 kg object attached to a spring is described by x=0.271 m ⋅ cos(0.512π⋅rad/s ⋅t) (Assume t is in seconds.) Find the amplitude of the motion. Find the spring constant. Find the position of the object at t = 0.324 s. Find the object's velocity at t = 0.324 s.

Chapter 3 Solutions

Fundamentals Of Physics

Ch. 3 - Can the sum of the magnitudes of two vectors ever...Ch. 3 - The two vectors shown in Fig. 3-21 lie in an xy...Ch. 3 - Being part of the Gators, the University of...Ch. 3 - Prob. 4Q Ch. 3 - Which of the arrangements of axes in Fig. 3-23 can...Ch. 3 - Prob. 6Q Ch. 3 - Prob. 7Q Ch. 3 - If ab=ac, must b equal c?Ch. 3 - If F = qv B and v is perpendicular to B, then...Ch. 3 - Figure 3-25 shows vector A and four other vectors...

Ch. 3 - In a game held within a three-dimensional maze,...Ch. 3 - The x and y components of four vectors a,b,c and d...Ch. 3 - Which of the following are correct meaningful...Ch. 3 - SSM What are a the x component and b the y...Ch. 3 - A displacement vector r in the xy plane is 15 m...Ch. 3 - SSM The x component of vector A is 25.0 m and the...Ch. 3 - Express the following angles in radians: a 20.0, b...Ch. 3 - A ship sets out to sail to a point 120 km due...Ch. 3 - In Fig. 3-27, a heavy piece of machinery is raised...Ch. 3 - Consider two displacements, one of magnitude 3 m...Ch. 3 - A person walks in the following pattern: 3.1 km...Ch. 3 - Prob. 9P Ch. 3 - Prob. 10P Ch. 3 - SSM a In unit-vector notation, what is the sum a ...Ch. 3 - A car is driven east for a distance of 50 km, then...Ch. 3 - A person desires to reach a point that is 3.40 km...Ch. 3 - You are to make four straight-line moves over a...Ch. 3 - SSM ILW WWW The two vectors a and b in Fig. 3-28...Ch. 3 - For the displacement vectors a=(3.0m)i+(4.0m)j and...Ch. 3 - GO ILW Three vectors a, b, and c each have a...Ch. 3 - Prob. 18P Ch. 3 - In a game of lawn chess, where pieces are moved...Ch. 3 - An explorer is caught in a whiteout in which the...Ch. 3 - GO An ant, crazed by the Sun on a hot Texas...Ch. 3 - a What is the sum of the following four vectors in...Ch. 3 - Prob. 23P Ch. 3 - Prob. 24P Ch. 3 - GO Oasis B is 25 km due east of oasis A. Starting...Ch. 3 - What is the sum of the following four vectors in a...Ch. 3 - GO If d+d2=5d3,d1d2=3d3, and d3=2 i +4 j , then...Ch. 3 - Two beetles run across flat sand, starting at the...Ch. 3 - GO Typical backyard ants often create a network of...Ch. 3 - GO Here are two vectors: a=(4.0m)i...Ch. 3 - Prob. 31P Ch. 3 - In Fig. 3-31, a cube of edge length a sits with...Ch. 3 - For the vectors in Fig. 3-32, with a = 4, b = 3,...Ch. 3 - Prob. 34P Ch. 3 - Two vectors, r and s, lie in the xy plane. Their...Ch. 3 - If d1=3i2j+4k and d2=5i+2jk, then what is...Ch. 3 - Prob. 37P Ch. 3 - GO For the following three vectors, what is...Ch. 3 - Prob. 39P Ch. 3 - GO Displacement d1 is in the yz plane 63.0 from...Ch. 3 - SSM ILW WWW Use the definition of scalar product,...Ch. 3 - Prob. 42P Ch. 3 - SSM ILW The three vectors in Fig. 3-33 have...Ch. 3 - Prob. 44P Ch. 3 - Vectors A and B lie in an xy plane. A has...Ch. 3 - Prob. 46P Ch. 3 - Vectors A and B lie in an xy plane. A has...Ch. 3 - GO Two vectors a and b have the components, in...Ch. 3 - SSM A sailboat sets out from the U.S. side of Lake...Ch. 3 - Vector d1 is in the negative direction of a y...Ch. 3 - Rock faults are ruptures along which opposite...Ch. 3 - Prob. 52P Ch. 3 - Prob. 53P Ch. 3 - For the vectors in Fig. 3-32, with a = 4, b = 3,...Ch. 3 - A particle undergoes three successive...Ch. 3 - Find the sum of the following four vectors in a...Ch. 3 - Prob. 57P Ch. 3 - A vector d has a magnitude of 2.5 m and points...Ch. 3 - A has the magnitude 12.0 m and is angled 60.0...Ch. 3 - Prob. 60P Ch. 3 - a In unit-vector notation, what is r = a b c if a...Ch. 3 - A golfer takes three putts to get the ball into...Ch. 3 - Prob. 63P Ch. 3 - SSM WWW A room has dimensions 3.00 m height 3.70...Ch. 3 - A protester carries his sign of protest, starting...Ch. 3 - Consider a in the positive direction of x, b in...Ch. 3 - Let i be directed to the east, j be directed to...Ch. 3 - A bank in downtown Boston is robbed see the map in...Ch. 3 - A wheel with a radius of 45.0 cm rolls without...Ch. 3 - A woman walks 250 m in the direction 30 east of...Ch. 3 - A vector d has a magnitude 3.0 m and is directed...Ch. 3 - A fire ant, searching for hot sauce in a picnic...Ch. 3 - Two vectors are given by a = 3.0 i 5.0 j and b =...Ch. 3 - Prob. 74P Ch. 3 - Find a north cross west, b down dot south, c east...Ch. 3 - A vector B, with a magnitude of 8.0 m, is added to...Ch. 3 - A man goes for a walk, starting from the origin of...Ch. 3 - What is the magnitude of a b a if a = 3.90, b =...Ch. 3 - In Fig. 3-38, the magnitude of a is 4.3, the...

Knowledge Booster

a) a → × b → b) a → . b → c) ( a → + b → ) . b → d) Component of a → along the direction of b →

Solution Summary: The author explains how vector calculation can be used to find the dot product, cross product as well as the mathrm.

To find:

a) $a→ ×b→$

b) $a→ .b→$

c) $(a→+b→) . b→$

d) Component of $a→$ along the direction of $b→$

Want to see the full answer?

Chapter 3 Solutions