The Vector ProductTwo vectors lying in the xy-plane are given by the equations A = 8î + 2j and B = -3î + 3j. Find Ax B and verify that Ã ×B = -B x A.SOLUTIONConceptualize 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 ) xî + 3jPerform the multiplication:ĀxB = 8î x (-3î) + 8î × 3j +|j x (-3î) + 2j xUse 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 2jUse the equations for the cross product of unit vectors evaluate the various terms:BxA =Therefore, Ax B = -B xAAs an alternative method for finding Ax B, you could useAXB = (AB - AB i+ (AB - ABz y)+y zхуTry it!EXERCISEWhat is the vector product of A = 4î + 3j - 5k and B = -6î + 8j + 7K? (Express your answer in vector form.)HintAxB =

Answered: Image /qna-images/answer/d3615a40-c610-4cf6-95f9-3ae1749c420a.jpg

ectors lying in the xy-plane are given by the equations A = 8i + 2j and B = -31 + 3j. Find AxB and verify that A xB = -B x A. ITION eptualize 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. gorize Because we use the definition of the cross product discussed in this section, we categorize this example as -Select--- problem. the cross product of the two vectors: AXB = i+ 2j) x i+ 3 rm the multiplication: ÂxB = 8i x (-3î) + 8î x 3j +| ]j × (-3î) + 2j × [ he equations for the cross product of unit vectors to evaluate the various terms: AxB = rify that A x B- -B xA, evaluate Bx A: BxA = (-31 + )x (8i + m the multiplication: BxA = (-3î) × ]i +(-3î) × 2j + 3j x 8i + jx 2j he equations for the cross product of unit vectors evaluate the various terms: BxA = fore, Ax B = -B × A alternative method for finding A xB, you could use AxB = (AB - A_B i + (AB - ABj+ (A B ECISE is the vector product of A = 41 + 3j – sk and B = -6i + 8j + ? (Express your answer in vector form.) Hint

ectors lying in the xy-plane are given by the equations A = 8i + 2j and B = -31 + 3j. Find AxB and verify that A xB = -B x A. ITION eptualize 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. gorize Because we use the definition of the cross product discussed in this section, we categorize this example as -Select--- problem. the cross product of the two vectors: AXB = i+ 2j) x i+ 3 rm the multiplication: ÂxB = 8i x (-3î) + 8î x 3j +| ]j × (-3î) + 2j × [ he equations for the cross product of unit vectors to evaluate the various terms: AxB = rify that A x B- -B xA, evaluate Bx A: BxA = (-31 + )x (8i + m the multiplication: BxA = (-3î) × ]i +(-3î) × 2j + 3j x 8i + jx 2j he equations for the cross product of unit vectors evaluate the various terms: BxA = fore, Ax B = -B × A alternative method for finding A xB, you could use AxB = (AB - A_B i + (AB - ABj+ (A B ECISE is the vector product of A = 41 + 3j – sk and B = -6i + 8j + ? (Express your answer in vector form.) Hint

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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Scalars and Vectors

Scalars and Vectors are the classification of physical quantities that are used to denote various terms in physics.

Question

The 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 Ã ×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 finding Ax B, you could use
AXB = (AB - AB i+ (AB - AB
z y)
+
y z
ху
Try it!
EXERCISE
What is the vector product of A = 4î + 3j - 5k and B = -6î + 8j + 7K? (Express your answer in vector form.)
Hint
AxB =

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