Consider the vectors a = (3,0, -4), b = (4, 5, 3), c = (0, 1, 0) € R^3. Find the angle between b and c. Find the area of the parallelogram defined by b and c. Find the volume of the parallelepiped defined by a, b and c.

Consider the vectors a = (3,0, -4), b = (4, 5, 3), c = (0, 1, 0) € R^3. Find the angle between b and c. Find the area of the parallelogram defined by b and c. Find the volume of the parallelepiped defined by a, b and c.

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter5: Inner Product Spaces

Section5.CR: Review Exercises

Problem 73CR

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Question

Consider the vectors a = (3,0, -4), b = (4, 5, 3), c = (0, 1, 0) € R^3.

Find the angle between b and c.

Find the area of the parallelogram defined by b and c.

Find the volume of the parallelepiped defined by a, b and c.

Quantities that have magnitude and direction but not position. Some examples of vectors are velocity, displacement, acceleration, and force. They are sometimes called Euclidean or spatial vectors.

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