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Consider the line parametrized by\(x= 4t + 2, y = t+2\)
Find vector \(\begin{pmatrix}a\\b\end{pmatrix}\) that's parallel to this line and satisfies \(a+b=10\).

 Feb 2, 2019
 #1
avatar+103947 
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Here's my best effort....although there might be an easier method !!!

 

Wnen  = 0   we have the point (2, 2)

When t = 1  we have the point  (6, 3)

So...the slope of the given line is   (3 - 2) / (6 - 2) =  1/4

 

If we let the parallel line go through the origin....we have the line  y = (1/4)x  

 

This means that  every point on this line has the coordinates ( x, 1/4x)

 

This implies that

 

x + (1/4)x = 10

 

(5/4)x = 10

 

x = 8   and y = (1/4)x = 2

 

So....the required vector  is    < 8, 2 >

 

 

cool cool cool

 Feb 2, 2019

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