vecor calculus 2

2010-12-04 6:40 am
1. Find a vector equation of the line tangent to the graph of r(t) = t^2 i - (1/(t+1)) j +(4-t^2) k at the point (4,1,0) on the curve.

2. Find vector equation of the tangent line at the point (-2,2,4) to the courve of the intersection of thre surface z-2x^2 - y^2 and the plane z=4.
更新1:

1. Find a vector equation of the line tangent to the graph of r(t) = (t^2) i - (1/(t+1)) j +(4-(t^2)) k at the point (4,1,0) on the curve. 2. Find vector equation of the tangent line at the point (-2,2,4) to the curve of the intersection of thre surface z=2x^2 - y^2 and the plane z=4.

更新2:

1. 點解知道代t=-2?? 係咪要令到r'(t)//r(t)???點知佢地平衡??

更新3:

平行 ......

更新4:

2.my standard answer is r(t)=(-2,2,4)+t(1,-2,0) 我都唔係好明點搵vector equation of tangent , 係咪好似第一題咁 (4,1,0) + s(-4,1,4)??? 第二題就 (-2,2,4)+s(-2,4,0)????

回答 (1)

2010-12-05 6:29 am
✔ 最佳答案
There are typo's in your question both (1) and (2). Please check.

2010-12-04 22:29:25 補充:
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圖片參考:http://img522.imageshack.us/img522/9230/73265343.png


2010-12-04 22:29:38 補充:
http://img522.imageshack.us/img522/9230/73265343.png

2010-12-06 22:01:38 補充:
(1) t^2 = 4; -1/(1+t) = 1; 4 - t^2 =0
t2=4=>t=+/-2
-1/(1+t)=1 =>t=-2
(2) My mistake again:
(x + 2)/(-2) = (y - 2)/4 = s/2
x = -s -2 ; y = 2s + 2
So (x,y,z) = (-2,2,4) + s(-1,2,0)


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