Chapter 9: Q. 5 (page 627)

True or False $||u \times v|| = ||u|| ||v|| \cos θ,$ where $θ$ is the angle between $u$ and $v$ .

Short Answer

Expert verified

The given statement is false.

Step by step solution

Step 1 Definition for cross product:

Cross product of two vectors is the method of multiplication of two vectors. A cross product is denoted by the multiplication sign $(\times)$ between two vectors. It is a binary vector operation, defined in a three-dimensional system. The cross product of two vectors is the third vector that is perpendicular to the two original vectors.

Step 2 Reason for the given statement being false:

It is false that, $||u \times v|| = ||u|| ||v|| \cos θ$ , where $θ$ is the angle between $u$ and $v$ . Because, the geometric properties of the cross product states that $||u \times v|| = ||u|| ||v|| \sin θ$ .

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True or False $||u \times v|| = ||u|| ||v|| \cos θ,$ where $θ$ is the angle between $u$ and $v$ .

Short Answer

Step by step solution

Step 1 Definition for cross product:

Step 2 Reason for the given statement being false:

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True or False u×v=uvcosθ,where θis the angle between uand v.

Short Answer

Step by step solution

Step 1 Definition for cross product:

Step 2 Reason for the given statement being false:

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

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Study anywhere. Anytime. Across all devices.

True or False $||u \times v|| = ||u|| ||v|| \cos θ,$ where $θ$ is the angle between $u$ and $v$ .