Question

Does the points P an Q lie on the given surface?

r(u,v) = <2u+3v, 1+5u-v, 2+u+v>
P(7,10,4) and Q(5,22,5)

Answer 1

can someone explain this question? :)

Answer 2

isn't r(u,x,v) or is it r(u,v) there is 3 number but we have 2 in r...

Answer 3

no it is r(u,v)

Answer 4

there is no variable given for the third component; what form is the equation in? cartesian or polar

Answer 5

i got it, zir confused me for a moment lol

Answer 6

yea i got it too but it needs 3 component anyway

Answer 7

its an exercise from parametric surface and their areas

Answer 8

r(u,v) = <2u+3v, 1+5u-v, 2+u+v>

given a point (x,y,z); does it satisfy these parts?

x = 2u+3v = 7
y = 1+5u-v=10
z = 2+u+v = 4

and


x = 2u+3v = 5
y = 1+5u-v= 22
z = 2+u+v = 5

Answer 9

2u+3v = 7
5u - v = 9
u + v = 2

now solve the equation and see if u and v are consistent throut them

Answer 10

i have also those equations :) owhhh oke.. so i can put this in a matrix right

Answer 11

matrix is fine, or regular substitution since they is simple enough

Answer 12

i gotta run to class, have fun and good luck ;)

Answer 13

5u - v = 9
v = 2 - u

5u - (2-u) = 9

5u - 2+u = 9

6u = 11

u = 11/6 perhaps

Answer 14

im back :) if u = 11/6, then v would have to be:

v = 2 - 11/6 = 1/6 so lets see if it fits the point:

2(11/6)+3(1/6) = 7

25/6 not = 7
----
5(11/6) - (1/6) = 9

54/6 = 9
----
11/6 + 1/6 = 2

12/6 = 2

well, at least we know those dont fit but we should try to solve it by using the 2 other combonations of equations just to dbl chk