a. Explanation Given information: The set of vectors u = 2 i − 3 j + k , v = i + j − 2 k and w = 3 i + 5 k . Formula used: The dot product of two vectors a = x i + y j + c k , b = l i + m j + n k is defined by multiplying the corresponding terms of i , j and k . The obtained product is scalar. Therefore, dot product is, a ⋅ b = x l + y m + z n The cross product of two vectors a = x i + y j + c k , b = l i + m j + n k is obtained by solving the determinant by writing the terms corresponding to i , j and k . The obtained product is a vector. Therefore, cross product is, a × b = i j k x y z l m n = i ( y n − z m ) − j ( x n − z l ) + k ( x m − y l ) Calculation: Consider, the set of vectors u = 2 i − 3 j + k , v = i + j − 2 k and w = 3 i + 5 k b. To determine To calculate: The value of the expression ( u ⋅ v ) × w for the set of vectors u = 2 i − 3 j + k , v = i + j − 2 k and w = 3 i + 5 k . c. To determine To calculate: The value of the expression ( u × v ) × w for the set of vectors u = 2 i − 3 j + k , v = i + j − 2 k and w = 3 i + 5 k . d. To determine To calculate: The value of the expression ( u ⋅ v ) × w for the set of vectors u = 2 i − 3 j + k , v = i + j − 2 k and w = 3 i + 5 k .

6th Edition

ISBN: 9781465208880

Author: SMITH KARL J, STRAUSS MONTY J, TODA MAGDALENA DANIELE

Publisher: Kendall Hunt Publishing

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Concept explainers

Percentage

A percentage is a number indicated as a fraction of 100. It is a dimensionless number often expressed using the symbol %.

Algebraic Expressions

In mathematics, an algebraic expression consists of constant(s), variable(s), and mathematical operators. It is made up of terms.

Numbers

Numbers are some measures used for counting. They can be compared one with another to know its position in the number line and determine which one is greater or lesser than the other.

Subtraction

Before we begin to understand the subtraction of algebraic expressions, we need to list out a few things that form the basis of algebra.

Addition

Before we begin to understand the addition of algebraic expressions, we need to list out a few things that form the basis of algebra.

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Question

Chapter 9, Problem 17PE

To determine

To calculate: The value of the expression (u×v)⋅w for the set of vectors u=2i−3j+k , v=i+j−2k and w=3i+5k .

To determine

To calculate: The value of the expression (u⋅v)×w for the set of vectors u=2i−3j+k , v=i+j−2k and w=3i+5k .

To determine

To calculate: The value of the expression (u×v)×w for the set of vectors u=2i−3j+k , v=i+j−2k and w=3i+5k .

To determine

To calculate: The value of the expression (u⋅v)×w for the set of vectors u=2i−3j+k , v=i+j−2k and w=3i+5k .

Expert Solution & Answer

Chapter 9 Solutions

Calculus

Ch. 9.1 - Prob. 1PS Ch. 9.1 - Prob. 2PS Ch. 9.1 - Prob. 3PS Ch. 9.1 - Prob. 4PS Ch. 9.1 - Prob. 5PS Ch. 9.1 - Prob. 6PS Ch. 9.1 - Prob. 7PS Ch. 9.1 - Prob. 8PS Ch. 9.1 - Prob. 9PS Ch. 9.1 - Prob. 10PS

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The value of the expression ( u × v ) ⋅ w for the set of vectors u = 2 i − 3 j + k , v = i + j − 2 k and w = 3 i + 5 k .

Solution Summary: The author calculates the value of the expression (utimes v)cdot w for the set of vectors.

Concept explainers

Videos

To calculate: The value of the expression (u×v)⋅w for the set of vectors u=2i−3j+k , v=i+j−2k and w=3i+5k .

To calculate: The value of the expression (u⋅v)×w for the set of vectors u=2i−3j+k , v=i+j−2k and w=3i+5k .

To calculate: The value of the expression (u×v)×w for the set of vectors u=2i−3j+k , v=i+j−2k and w=3i+5k .

To calculate: The value of the expression (u⋅v)×w for the set of vectors u=2i−3j+k , v=i+j−2k and w=3i+5k .

Chapter 9 Solutions