I've started out with vectors and am still touching the surface of the topic, however I'm having an issue with a relatively simple question.
Find a vector of magnitude 27 units which is parallel to $a = 3i+4j$
I scouted around and found a few methods however I still can't seem to get around it, probably due to my lack of understanding of the topic so far. Could someone kindly work or explain the problem and how to solve it?
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$\begingroup$$\vec{a}$ is a vector which you can represent as a line from (0,0) to the point (3,4). By Pythagoras the length of the line is 5. Joining any two points along that line will give you a vector in the same direction as $\vec{a}$.
You want a vector with magnitude 27, so you can just join (0,0) to the point 27/5*(3,4) i.e. to (81/5, 108/5).
Your vector would be $$ \frac{81}{5} \vec{i} + \frac{108}{5} \vec{j}. $$
$\endgroup$ 1 $\begingroup$This looks to me a like a classic situation where getting a large sheet of squared paper plus fine-point pen or pencil, and plotting out the vectors will help.
Start with the one you have, then draw in some others parallel to that vector at various locations, making them 27 times longer (having chosen fine-squared paper will help here!), and check their co-ordinates.
You should soon start to get a feel of the whole idea after a few minutes of doing this.
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