Find values of a making one vector parallel to the other

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To determine the values of "a" that make vector v = 4ai - 2j parallel to vector w = a^2i + 4j, one must use the condition that two vectors are parallel if their cross product is zero or if one is a scalar multiple of the other. The discussion highlights the approach of using the dot product and magnitude to find the necessary conditions for parallelism. Participants suggest that solving for "a" can be approached by finding a vector perpendicular to v and using the condition u.w = 0. Ultimately, the key is to manipulate the equations to isolate "a" effectively.
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Find values of "a" making one vector parallel to the other

Homework Statement



Find the value(s) of a making vector v = 4ai - 2j, parallel to vector w = a^2i +4j

Homework Equations


P= (a dot b/ magnitude b^2) (bi, bj)


The Attempt at a Solution


I can plug and chug, but at what point do you solve for a?
 
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If you can find a vector that's perpendicular to v, then you can just plug and chug on finding when u.w=0.
 

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