- #1

member 508213

## Homework Statement

I am supposed to find the tangent and normal unit vector to r(t)=<2sint,5t,cost>.

## Homework Equations

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## The Attempt at a Solution

r1(t)=<2cost,5,-sint> which is a tangent vector to the curve, and then to make it a unit vector I would multiply by 1/(sqrt(4cos^2t+25+sin^2t).

Finding the normal unit vector is a little bit more confusing for me. I understand that it is supposed to be the derivative of the tangent vector divided by the magnitude (to make it length 1) but I am surprised because taking the derivatives of <2cost/sqrt(4cos^2t+25+sin^2t), 5/sqrt(4cos^2t+25+sin^2t),-sint/sqrt(4cos^2t+25+sin^2t)> and then turning that into a unit vector is extremely messy. Would it be possible to instead simply take the derivative of the tangent vector (not the

**unit**tangent vector) r1(t)=<2cost,5,-sint> and get r2(t)=<-2sint,0,-cost> and then make that into a unit vector by dividing by sqrt(4sin^2t+cos^2t) or would this be incorrect.

Thanks