For the following exercises, determine whether the statement is true or false. Justify the answer with a proof or a counterexample.
423. For
Determine whether the statement is true or false. Justify the answer with a proof or a counterexample.
Explanation of Solution
Given information:
For vector
From the given information we know that for vector
We consider
Then we can find dot product as follows.
By the definition of scalar multiplication we can figure out the vector
Therefore the dot product
From (1) and (2) we can say that,
Hence the statement “For vector
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