Answer to Question #124674 in Calculus for Rebecca Kemunto

Question #124674
Find the unit tangent vector to any point on the curve
r=(t^2+1)I+(4t-3)j+(2t^2-6t)k
1
Expert's answer
2020-06-30T18:43:02-0400

Given r=(1+t2)i^+(4t3)j^+(2t26t)k^r =(1+t^2)\hat{i} + (4t-3)\hat{j} + (2t^2-6t)\hat{k}

differentiating it with respect to t,

r=2ti^+4j^+(4t6)k^r' = 2t\hat{i} + 4\hat{j} + (4t-6)\hat{k}

unit tangent vector,

r^=rr=2ti^+4j^+(4t6)k^4t2+16+(4t6)2\hat{r'} = \frac{\vec{r'}}{|r'|} = \frac{2t\hat{i} + 4\hat{j} + (4t-6)\hat{k}}{\sqrt{4t^2 + 16 + (4t-6)^2}} =2ti^+4j^+(4t6)k^(20t212t+52)=ti^+2j^+(2t3)k^(5t23t+13)=\frac{2t\hat{i} + 4\hat{j} + (4t-6)\hat{k}}{\sqrt{(20t^2-12t+52)}} = \frac{t\hat{i} + 2\hat{j} + (2t-3)\hat{k}}{\sqrt{(5t^2-3t+13)}}


Need a fast expert's response?

Submit order

and get a quick answer at the best price

for any assignment or question with DETAILED EXPLANATIONS!

Comments

No comments. Be the first!

Leave a comment