a. Let a = ⟨0, 1, 0⟩ , let r = ⟨x, y, z⟩ , and consider the rotation field F = a x r. Use the right-hand rule for cross products to find the direction of F at the points (0, 1, 1), (1, 1, 0), (0, 1, -1), and (-1, 1, 0).b. With a = ⟨0, 1, 0⟩ , explain why the rotation field F = a x r circles the y-axis in the counterclockwise direction looking along a from head to tail (that is, in the negative y-direction).

a. Let a = ⟨0, 1, 0⟩ , let r = ⟨x, y, z⟩ , and consider the rotation field F = a x r. Use the right-hand rule for cross products to find the direction of F at the points (0, 1, 1), (1, 1, 0), (0, 1, -1), and (-1, 1, 0).b. With a = ⟨0, 1, 0⟩ , explain why the rotation field F = a x r circles the y-axis in the counterclockwise direction looking along a from head to tail (that is, in the negative y-direction).

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter6: Linear Transformations

Section6.2: The Kernewl And Range Of A Linear Transformation

Problem 59E: Let T:R3R3 be the linear transformation that projects u onto v=(2,1,1). (a) Find the rank and...

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