Whether the statement “If the magnitude of two
Answer to Problem 67E
The statement “If the magnitude of two vectors are doubled, then the magnitude of their cross product is also doubled.” is false.
Explanation of Solution
Given information:
The statement “If the magnitude of two vectors are doubled, then the magnitude of their cross product is also doubled.”
Consider the provided statement “If the magnitude of two vectors are doubled, then the magnitude of their cross product is also doubled.”
Let
Mathematically the magnitude of cross product is expressed as,
According to the question, magnitude of vectors are doubled, therefore,
Now, the magnitude of cross product is,
If the magnitude of two vectors are doubled, then the magnitude of their cross product becomes four time of the original one.
Thus, the statement “If the magnitude of two vectors are doubled, then the magnitude of their cross product is also doubled.” is false.
Chapter 11 Solutions
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