Question

for the helix r(t) = sin(t)i + cos(t)i + tk

(a) find the angle between the helix and the plane at the point of intersection

Answer 1

\[cos (theta) = \frac{(-i +k)(k)}{|-i +k||k|}\]

Answer 2

i got up to here

Answer 3

but im having probvs solving this.

Answer 4

i just just need to solve that eqn above

dw about the question

Answer 5

i forgot how to solve cos(theta) blah blah

Answer 6

the answer is \[\frac{1}{sqrt(2)}\]

Answer 7

but how do i get that???

Answer 8

where is the plane ?

Answer 9

normal to the plane is k

Answer 10

i have already done that step

Answer 11

i neeed help with [\cos(theta) = \frac{(-i+k)(k)}{| -i + k||k|}\]

Answer 12

darn it latex fail

Answer 13

ahh thats easy then

Answer 14

|-i+k| = sqrt(1^2 + 1^2) = sqrt(2)

|k| = 1

Answer 15

(-i+k) . (k) = -i.k + k . k = 0 + 1 = 1

Answer 16

OHHH

Answer 17

its a dot product ^

Answer 18

ya OHHHHH smh at the person who supposedly knows everything

Answer 19

(-i)(k) = 0?

Answer 20

-i . k = 0
cuz i and k are defined to be perpendicular