Question 1189550
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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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<pre>
Notice that vectors A and B have THE SAME magnitude


    |A| = {{{sqrt(2^2+4^2+1^2)}}} = {{{sqrt(4+16+1)}}} = {{{sqrt(17)}}},

    |B| = {{{sqrt(4^2+2^2+1^2)}}} = {{{sqrt(16+4+1)}}} = {{{sqrt(17)}}}.


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.


<U>ANSWER</U>.  There is ONLY ONE such a vector: it is vector A itself.
</pre>

Solved and explained.


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<H3>Post-solution note</H3> :  

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