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# Vector Calculus: Finding the vector equation of the line tangent to r(t) at point P

Posted on 2011-09-19

Find a vector equation of the line tangent to the graph of r(t) at the point P on the curve:

**r**(t) = (2t-1)**i** + sqrt(3t+4)**j** ; P(-1,2)

The answer I got was:

**T**(t) =

**r**'(t) / || **r**'(t) || =

<2, 3/2(3t+4)^(-1/2)>

/

sqrt(4 + ( 9 / (12t + 16) )

Not sure if the above is right. First time my professor said it was wrong, then claimed it was right, but when asked a third time to see if it really was, never got a clear answer so I'm confused.