SOLUTION: if A=2i+4j+k and B=4i+2j+k find the vector x parallel to A and have magnitude of B?

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Question 1189550: if A=2i+4j+k and B=4i+2j+k find the vector x parallel to A and have magnitude of B?
Answer by ikleyn(52786) About Me  (Show Source):
You can put this solution on YOUR website!
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if A=2i+4j+k and B=4i+2j+k find the vector x parallel to A and have magnitude of B?
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Notice that vectors A and B have THE SAME magnitude


    |A| = sqrt%282%5E2%2B4%5E2%2B1%5E2%29 = sqrt%284%2B16%2B1%29 = sqrt%2817%29,

    |B| = sqrt%284%5E2%2B2%5E2%2B1%5E2%29 = sqrt%2816%2B4%2B1%29 = sqrt%2817%29.


Thus, the problem asks to find vector x parallel to A and having the same magnitude as A.


There is ONLY ONE such a vector: it is vector A itself.


ANSWER.  There is ONLY ONE such a vector: it is vector A itself.

Solved and explained.

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Post-solution note

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        In my solution,  I do not consider  ANTI-parallel vector  -A  as a parallel to  A.