Question

A unit tangent vector to the surface x=t,y=t²,z=t³ at t= 1 is_

Answer 1

Step-by-step explanation:

unit vector

VectorU = [x(icap) + y(jcap)+ z(kcap)] / √( x²+y²+z²)

=[ t(Icap)+t²(jcap)+t³(kcap)] / √( t²+t⁴+t^6)

at t=1

vector U= i( cap+j cap+ k cap) / √3.

Answer

Answer 2

( i + j + k) / √3  is unit tangent vector to the surface x=t,y=t²,z=t³ at t= 1

Step-by-step explanation:

A unit tangent vector to the surface x=t,y=t²,z=t³

= (xi + yj + zk) /√(x² + y² + z² )

= ( ti + t²j  + t³k ) / √((t)² + (t²)² + (t³)² )

putting t = 1

= ( i + j + k) /  √(1 +1 + 1 )

= ( i + j + k) / √3

( i + j + k) / √3  is unit tangent vector to the surface x=t,y=t²,z=t³ at t= 1

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