Find the unit tangent vector t(t) at the point with the given value of the parameter t. r(t)

Since the equation was missing, I solved it with another equation and got an answer of T(0) = <3j / 5 + 4k / 5>.

Please see my explanation. I hope this helps

Step-by-step explanation:

The question asked us to find out unit tangent vector.

Recall unit vector = vector / magnitude of vector

Since the question is missing with an equation. I suppose an equation.

r(t)=Cost i, 3t j, 2Sin(2t) k at t=0

Lets take out differentiation

r'(t) = <(-Sint), 3, 2(Cos(2t)(2))>

r'(t)= <-Sint, 3, 4Cos(2t)>

Now substitute t=0 in the differentiate found above.

r'(0)= <-Sin(0), 3, 4Cos(2*0)>

r'(0)= <0, 3, 4(1)>

r'(0)= <0,3,4>

vector r'(0)=<0i, 3j, 4k>

Now lets find out magnitude of vector

|r'(0)| =

|r'(0)| =

|r'(0)| =

|r'(0)| = 5

Unit Tangent Vector

T(0) = <0, 3, 4> / 5

T(0) = <3j / 5  +  4K / 5>