Question

Find the point P on the curve r(t) that lies closest to Po and state the distance between Po and P. r(t) = t²i+2tj + 2tk; Po(4,7,20) The point P is (D). (Type an ordered triple, using integers or decimals.)

Answer 1

To find the point P on the curve r(t) that is closest to Po, we can use the formula for the distance between two points in three-dimensional space. We can then find the point P by finding the value of t that minimizes the distance d.

Step-by-step explanation:

To find the point P on the curve r(t) that is closest to Po, we can use the formula for the distance between two points in three-dimensional space:

d = sqrt((x2 - x1)^2 + (y2 - y1)^2 + (z2 - z1)^2)

In this case, the coordinates of Po are (4, 7, 20). We can substitute these values into the formula to find the distance between Po and P.

We can then find the point P by finding the value of t that minimizes the distance d. This can be done by taking the derivative of the distance formula with respect to t, setting it equal to zero, and solving for t.

Finally, we can substitute the value of t into the equation for r(t) to find the coordinates of P, which will be the closest point on the curve to Po.