Consider A = ⟨0, 4, 2⟩ ,B =, ⟨6,−1, 0⟩ and C = ⟨3, 0, 1⟩. (a) Find the unit vector having the same direction as B − 2A + 1/2 C. (b) Draw the vector that you get in (a). (c) Find scalars a, b and c such that aA + bB = (c − 1)C.

Consider A = ⟨0, 4, 2⟩ ,B =, ⟨6,−1, 0⟩ and C = ⟨3, 0, 1⟩. (a) Find the unit vector having the same direction as B − 2A + 1/2 C. (b) Draw the vector that you get in (a). (c) Find scalars a, b and c such that aA + bB = (c − 1)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 13CR

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Question

Consider A = ⟨0, 4, 2⟩ ,B =, ⟨6,−1, 0⟩ and C = ⟨3, 0, 1⟩.
(a) Find the unit vector having the same direction as B − 2A + 1/2 C.
(b) Draw the vector that you get in (a).
(c) Find scalars a, b and c such that aA + bB = (c − 1)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.

Expert Solution