The angle of intersection of a curve and a plane is defined as (pi/2-?), where?is the angle between a tangent to the curve and a normal to the plane at the point of intersection. Find the cosine of the angle of intersection of the twisted cubic r(t)= with the plane 2x-2y+3z=2. Solution use intersection the value of t=1 T(t)=r\'(t)/modulus of r\'(t) =[i+2j+k]/sqrt6 and normal vector is 2i-2j+3k cos(angle)=1/12sqrt6.

1. The angle of intersection of a curve and a plane is defined as (pi/2-?), where?is the angle
between a tangent to the curve and a normal to the plane at the point of intersection. Find the
cosine of the angle of intersection of the twisted cubic r(t)= with the plane 2x-2y+3z=2.
Solution
use intersection the value of t=1 T(t)=r'(t)/modulus of r'(t) =[i+2j+k]/sqrt6
and normal vector is 2i-2j+3k cos(angle)=1/12sqrt6