Let `C:r(t)=x(t)hati+y(t)hatj+z(t)hatk` be a differentiable curve, i.e., `lim_(xto0) (r(t+H)-r(h))/(h)` exist for all t,
`therefore r'(t)=x'(t)hati+y'(t)hatj+z'(t)hatk`
Iff `r'(t)`, is tangent to the curve C at the point `P[x(t),y(t),z(t)] and r'(t)` points in the direction of increasing t.
Q. The tangent vector to `r(t)=2t^(2)hati+(1-t)hatj+(3t^(2)+2)hatk` at (2,0,5) is

Let C:r(t)=x(t)hati+y(t)hatj+z(t)hatk be a differentiable curve, i.e., lim_(xto0) (r(t+H)-r(h))/(h) exist for all t, therefore r'(t)=x'(t)hati+y'(t)hatj+z'(t)hatk Iff r'(t) , is tangent to the curve C at the point P[x(t),y(t),z(t)] and r'(t) points in the direction of increasing t. Q. The point P on the curve r(t)=(1-2t)hati+t^(2)hatj+2e^(2(t-1))hatk at which the tangent vector r'(t) is parallel to the radius vector r(t) is

Let C:r(t)=x(t)hati+y(t)hatj+z(t)hatk be a differentiable curve, i.e., lim_(xto0) (r(t+H)-r(h))/(h) exist for all t, therefore r'(t)=x'(t)hati+y'(t)hatj+z'(t)hatk Iff r'(t) , is tangent to the curve C at the point P[x(t),y(t),z(t)] and r'(t) points in the direction of increasing t. Q. The point P on the curve r(t)=(1-2t)hati+t^(2)hatj+2e^(2(t-1))hatk at which the tangent vector r'(t) is parallel to the radius vector r(t) is

Let C:vecr(t)=x(t)hati+y(t)hatj+z(t)hatk be a differentiable curve, i.e. exists lim_(hto0) (vecr(t+h)-vecr(t))/(h) AA t therefore vecr'(t)=x'(t)hati+y'(t)hatj+z'(t)hatk vecr'(t) is tangent to the curve C at the point P[x(t),y(t),z(t)] and points in the direction of increasing t . The tangent vector to vecr(t)=(2t^(2))hati+(1-t)hatj+(3t^(2)+2)hatk at (2,0,5) is:

Let C:vecr(t)=x(t)hati+y(t)hatj+z(t)hatk be a differentiable curve, i.e. exists lim_(hto0) (vecr(t+h)-vecr(t))/(h) AA t therefore vecr'(t)=x'(t)hati+y'(t)hatj+z'(t)hatk vecr'(t) is tangent to the curve C at the point P[x(t),y(t),z(t)] and points in the direction of increasing t . The tangent vector to vecr(t)=(2t^(2))hati+(1-t)hatj+(3t^(2)+2)hatk at (2,0,5) is:

Let C:vecr(t)=x(t)hati+y(t)hatj+z(t)hatk be a differentiable curve i.e., exists lim_(hto0) (vecr(t+h)-vecr(t))/(h) forall t therefore vecr'(t)=x'(t)hati+y'(t)hatj+z'(t)hatk vecr'(t) is tangent to the curve C at the point P[x(t),y(t),z(t)], vecr'(t) points in the direction of increasing t . The point P on the curve vecr(t)=(1-2t)hati+t^(2)hatj+2e^(2(t-1))hatk at which the tangent vector vecr'(t) is parallel to the radius vector vecr(t) is:

Let C:vecr(t)=x(t)hati+y(t)hatj+z(t)hatk be a differentiable curve i.e., exists lim_(hto0) (vecr(t+h)-vecr(t))/(h) forall t therefore vecr'(t)=x'(t)hati+y'(t)hatj+z'(t)hatk vecr'(t) is tangent to the curve C at the point P[x(t),y(t),z(t)], vecr'(t) points in the direction of increasing t . The point P on the curve vecr(t)=(1-2t)hati+t^(2)hatj+2e^(2(t-1))hatk at which the tangent vector vecr'(t) is parallel to the radius vector vecr(t) is:

A unit tangent vector at t=2 on the curve x=t^(2)+2, y=4t-5 and z=2t^(2)-6t is

A unit tangent vector at t=2 on the curve x=t^(2)+2, y=4t-5 and z=2t^(2)-6t is

A unit tangent vector at t=2 on the curve x=t^(2)+2, y=4t-5 and z=2t^(2)-6t is