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

University Physics Volume 1

18th Edition

ISBN:9781938168277

Author:William Moebs, Samuel J. Ling, Jeff Sanny

Publisher:William Moebs, Samuel J. Ling, Jeff Sanny

Chapter2: Vectors

Section: Chapter Questions

Problem 91CP: between points in a plane do not change when a coordinate system is rotated In other words, the...

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