find the equation of the normal plane and osculating plane of the curve at the given point
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We have recently defined three types of planes known as Normal, Rectifying, and Osculating Planes. Let r⃗ (t)=(x(t),y(t),z(t))be a vector-valued function and P0(x0,y0,z0) be a point on a curve C generated by the vector-valued function r⃗ (t0).
The Normal Plane of P: is perpendicular to T^(t0)=N^(t0)×B^(t0)and passes through P0(x0,y0,z0).
The Rectifying Plane of P is perpendicular to N^(t0)=B^(t0)×T^(t0)and passes through P0(x0,y0,z0).
The Osculating Plane of P is perpendicular to B^(t0)=T^(t0)×N^(t0)and passes through P0(x0,y0,z0).
We should note that the normal plane of P is perpendicular to r′→(t0).
The Normal Plane of P: is perpendicular to T^(t0)=N^(t0)×B^(t0)and passes through P0(x0,y0,z0).
The Rectifying Plane of P is perpendicular to N^(t0)=B^(t0)×T^(t0)and passes through P0(x0,y0,z0).
The Osculating Plane of P is perpendicular to B^(t0)=T^(t0)×N^(t0)and passes through P0(x0,y0,z0).
We should note that the normal plane of P is perpendicular to r′→(t0).
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