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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| = = = ,
|B| = = = .
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.