Home
Class 12
MATHS
Let C:r(t)=x(t)hati+y(t)hatj+z(t)hatk be...

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

Promotional Banner

Similar Questions

Explore conceptually related problems

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:

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 tangent vector to r(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) 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:

Find the locus of the point (t^(2)-t+1,t^(2)+t+1),t in R

Find the locus of the point (t^2-t+1,t^2+t+1),t in R .

Find the locus of the point (t^2-t+1,t^2+t+1),t in R .

For the curve x=t^(2)-1, y=t^(2)-t , the tangent is parallel to X-axis at the point where