Question

Determine the point at which the function r(t) = has a tagent line that is perpendicular to the plane 4x+y-2z=12...

Answer 1

normal vector of plane is (4,1,-2)

Answer 2

direction vector of tangent to r(t) is <t^2, 4, 2t>

?

Answer 3

\[\large \dfrac{t^2}{4} = \dfrac{4}{1} = \dfrac{2t}{-2}\]

solve \(\large t\)

Answer 4

How do we solve for t? By putting in (4,1,-2)? @ganeshie8

Answer 5

take the last two ratios :
\[\large \dfrac{4}{1} = \dfrac{2t}{-2}\]

cross multiply and solve \(\large t\)

Answer 6

t = -4?

Answer 7

yes! plug that in first two rations and see if it satisfies

Answer 8

The first two rations? You mean ratios?

Answer 9

yes

Answer 10

Okay I did the math and yes it does. :)

Answer 11

Taking care of neighbors kid..sorry :/