Explanation Given: The diagram: Proof: Let the two vectors be: v = v 1 i + v 2 j + v 3 k , w = w 1 i + w 2 j + w 3 k Let us represent the cross product of these two vectors: v × w = [ i j k v 1 v 2 v 3 w 1 w 2 w 3 ] = ( v 2 w 3 −

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ISBN: 9781319323394

Author: Rogawski

Publisher: MAC HIGHER

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Coordinate Geometry

Coordinate geometry, also known as analytic geometry or Cartesian geometry in classical mathematics, is a type of geometry that is studied using a coordinate system. Coordinate geometry is a branch of mathematics that describes the position of points on …

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Chapter 13.4, Problem 59E

To determine

To prove:

That the absolute value of the k component of the product $v \times w$ is equal to area of parallelogram spanned by the projections $v_{o} and w_{o}$ onto the x-y plane.

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Chapter 13.4, Problem 58E

Chapter 13.4, Problem 60E

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Chapter 13 Solutions

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Ch. 13.1 - Prob. 1PQ Ch. 13.1 - Prob. 2PQ Ch. 13.1 - Prob. 3PQ Ch. 13.1 - Prob. 4PQ Ch. 13.1 - Prob. 5PQ Ch. 13.1 - Prob. 6PQ Ch. 13.1 - Prob. 1E Ch. 13.1 - Prob. 2E Ch. 13.1 - Prob. 3E Ch. 13.1 - Prob. 4E

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To prove: That the absolute value of the k component of the product v × w is equal to area of parallelogram spanned by the projections v o and w o onto the x-y plane.

Solution Summary: The author explains that the absolute value of k component of the product v w is equal to area of parallelogram spanned by the projections

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To prove:

That the absolute value of the k component of the product $v \times w$ is equal to area of parallelogram spanned by the projections $v_{o} and w_{o}$ onto the x-y plane.

Want to see the full answer?

Chapter 13 Solutions

To prove: That the absolute value of the k component of the product v × w is equal to area of parallelogram spanned by the projections v o and w o onto the x-y plane.

Solution Summary: The author explains that the absolute value of k component of the product v w is equal to area of parallelogram spanned by the projections

Concept explainers

Videos

To prove: That the absolute value of the k component of the product v×w is equal to area of parallelogram spanned by the projections vo and wo onto the x-y plane.

Want to see the full answer?

Chapter 13 Solutions

To prove:

That the absolute value of the k component of the product $v \times w$ is equal to area of parallelogram spanned by the projections $v_{o} and w_{o}$ onto the x-y plane.