The curves r1(t) = 4t, t2, t3 and r2(t) = sin(t), sin(5t), 2t intersect at the origin. find their angle of intersection, θ, correct to the nearest degree.

First get the tangent vectors by differentiating r1 and r2 

Evaluate at t=0


Use identity for angle between 2 vectors:


Evaluate dot product and unit vectors:


Sub into identity and solve for theta:


Angle of intersection is about 79 degrees.

Answer: 900°

good luck on your studies! : )

david edward.

Y’all got to do it all over