Explain why or why not Determine whether the

Chapter 10, Problem 41E

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QUESTION:

Explain why or why not Determine whether the following statements are true and give an explanation or counterexample.

a. The cross product of two nonzero vectors is a nonzero vector.

b. \(|\mathbf{u} \times \mathbf{v}|\) is less than both |u| and |v|.

c. If u points east and v points south, then \(\mathbf{u} \times \mathbf{v}\) points west.

d. If  \(\mathbf{u} \times \mathbf{v}\) = 0 and \(\mathbf{u} \cdot \mathbf{v}\) = 0, then either u = 0 or v = 0 (or both).

e. Law of Cancellation? If \(\mathbf{u} \times \mathbf{v}=\mathbf{u} \times \mathbf{w}\), then v = w.

Questions & Answers

QUESTION:

Explain why or why not Determine whether the following statements are true and give an explanation or counterexample.

a. The cross product of two nonzero vectors is a nonzero vector.

b. \(|\mathbf{u} \times \mathbf{v}|\) is less than both |u| and |v|.

c. If u points east and v points south, then \(\mathbf{u} \times \mathbf{v}\) points west.

d. If  \(\mathbf{u} \times \mathbf{v}\) = 0 and \(\mathbf{u} \cdot \mathbf{v}\) = 0, then either u = 0 or v = 0 (or both).

e. Law of Cancellation? If \(\mathbf{u} \times \mathbf{v}=\mathbf{u} \times \mathbf{w}\), then v = w.

ANSWER:

Solution 41EStep 1 of 4:a) The given statement “ the cross product of two nonzero vectors is a nonzero vector” is false.Because , we know that ‘i’ is the unit vector along x -axis.So , it is non zero vector and it is parallel to itself , the angle between i and i is 0.Hence , by the definition of the cross product , we see that = |i| |i| sin(0) = (1) (1) (0) = 0.

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