Homework SourseConsider the curve rt At what points xyz does the vector tan
Consider the curve r(t)= <2t+1,t-cost,sint> At what points (x,y,z) does the vector tangent to the curve point in the direction of i=<1,0,0>? There may be more than one point.
Solution
r(t) = <2t+1, t-cost, sint>
r \' (t) = < 2, 1 + sint, cost>
For the tangent to be in the direction of <1, 0, 0>
r \' (t) = k* <1, 0, 0>
< 2, 1 + sint, cost> = <k, 0, 0>
=> k = 2
1 + sint = 0 and cost = 0
sint = -1 and cost = 0
t = 2npi + 3pi/2 for n in Integers.
Points (x, y, z) are,
r(t) = <2t+1, t-cost, sint>
= < 2* (2npi + 3pi/2) + 1, 2npi + 3pi/2 - 0, -1>
= < 4npi + 3pi + 1, 2npi + 3pi/2, -1> for all n in Integers.
