Explanation Concept Used: 1. Cross product (vector product) of two vectors a → = { a x ; a y ; a z } and b → = { b x ; b y ; b z } in Cartesian coordinate system is a vector defined by: a → × b → = | i j k a x a y a z b x b y b z | = i ( a y b z − a z b y ) − j ( a x b z − a z b x ) + k ( a x b y − a y b x ) Also, a → × b → = − b → × a → 2. Formula for vector triple product: ( a → × b → ) × c → = ( a → ⋅ c → ) b → − ( b → ⋅ c → ) a → Vectors u , v a n d w are given, and we need to prove that: u × ( v × w ) + v × ( w × u ) + w × ( u × v ) = 0 To prove this we proceed as follows: Using the definition of vector triple product, we have: u × ( v × w ) = − ( v × w ) × u = − [ ( v ⋅ u ) w − ( w ⋅ u ) v ] = ( w ⋅ u ) v − ( v ⋅ u ) w ⇒ u × ( v × w ) = ( w ⋅ u ) v − ( v ⋅ u ) w Similarly, v × ( w x

Student's Solution and Survival Manual for Calculus

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ISBN: 9781524934040

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

Publisher: Kendall Hunt Publishing

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System that uses coordinates to uniquely determine the position of points. The most common coordinate system is the Cartesian system, where points are given by distance along a horizontal x-axis and vertical y-axis from the origin. A polar coordinate system locates a point by its direction relative to a reference direction and its distance from a given point. In three dimensions, it leads to cylindrical and spherical coordinates.

Chapter 9.4, Problem 57PS

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To prove: formula for vector product: u×(v×w)+v×(w×u)+w×(u×v)=0 .

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Chapter 9.4, Problem 56PS

Chapter 9.4, Problem 58PS

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7. Show that the vectors A=4a, -2a, +2a, and B = -6ā, +3ā, -3ā, are parallel to each other.

Chapter 9 Solutions

Student's Solution and Survival Manual for Calculus

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To prove: formula for vector product: u × ( v × w ) + v × ( w × u ) + w × ( u × v ) = 0 .

Solution Summary: The author explains the formula for vector product: utimes w+v times (w)+w times (u)=0.

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To prove: formula for vector product: u×(v×w)+v×(w×u)+w×(u×v)=0 .

Want to see the full answer?

Chapter 9 Solutions