Find the curve's unit tangent vector. Also, find the length

Sam Longoria

Sam Longoria

Answered question

2021-12-20

Find the curves

Answer & Explanation

Wendy Boykin

Wendy Boykin

Beginner2021-12-21Added 35 answers

Given
r(t)=6t3i+2t3j+3t3k, 1t2
r(t)=18t2i+6t2j+9t2k
|r(t)|=(18t2)2+(6t2)2+(9t2)2
=9t4(36+4+9)
=21t2
unit vector =r(t)|r(t)|=18t2i+6t2j+9t2k21t2
=67i+221j+37k
Lenght of curve:
=ab|r(t)|dt
=1221t2dt
=21[t33]12
=7(81)
=49 units
Elois Puryear

Elois Puryear

Beginner2021-12-22Added 30 answers

The j component should (2/7)j not (2/21)j
nick1337

nick1337

Expert2021-12-28Added 777 answers

Yes, you are correct.

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?