Solution Found!
Explain why or why not Determine whether the
Chapter 10, Problem 41E(choose chapter or problem)
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.