Thread: vector problems

1] how to find the unit tangent vector T(t)at the indicated point of the vector function r(t)=(e^(8t) cos(t)) i + (e^(8t)sin(t)) j + (e^(8t)) k ,what is ?

>> i am not sure, but i kind of think that it should be derivative and divided by the magnitude.. but somehow it cannot be done, please help!!!


And also 2] how to find parametric equations for the tangent line at the point on the curve ?

>> i totally get lost from the question.. can someone please help?

Originally Posted by iwonder

1] how to find the unit tangent vector T(t)at the indicated point of the vector function r(t)=(e^(8t) cos(t)) i + (e^(8t)sin(t)) j + (e^(8t)) k ,what is ?

>> i am not sure, but i kind of think that it should be derivative and divided by the magnitude.. but somehow it cannot be done, please help!!!

[snip]

A vector tangent to the curve defined by r(t) is . Substitute and divide the resulting vector by its magnitude.

Originally Posted by iwonder

[snip]
And also 2] how to find parametric equations for the tangent line at the point on the curve ?

>> i totally get lost from the question.. can someone please help?

A vector tangent to the curve has i, j and k components given respectively by , , .

So at a vector in the direction of the tangent is ......

And a point on the tangent is obviously .

So you have a vector in the direction of the line and a point on the line. You should know how to get the parametric equations of the line from these two things.