<PRE><B>Question 1147491</B>
&lt;br&gt;
A vector parallel to &lt;3,5&gt; is of the form &lt;3a,5a&gt;.&lt;br&gt;
A vector perpendicular to &lt;3,5&gt; is of the form &lt;5b,-3b&gt;.  (The dot product has to be 0.)&lt;br&gt;
We want &lt;3a,5a&gt; + &lt;5b,-3b&gt; to be equal to &lt;4,1&gt;.&lt;br&gt;
{{{3a+5b = 4}}}
{{{5a-3b = 1}}}&lt;br&gt;
{{{9a+15b = 12}}}
{{{25a-15b = 5}}}
{{{34a = 17}}}
{{{a = 1/2}}}
{{{b = 1/2}}}&lt;br&gt;
ANSWER: v1 = &lt;3/2,5/2&gt;; v2 = &lt;5/2,-3/2&gt;  --&gt;  v1+v2 = &lt;8/2,2/2&gt; = &lt;4,1&gt;</PRE>