00:02
In this question, we are given a curve rt is equal to t squared r -capped plus t j -cap plus t k -cap.
00:14
We need to obtain a point p on this curve such that distance d of p from point p -0, where p -0 is given by 1, 5, and 11.
00:36
Is minimum.
00:41
Now any point on this curve is given by p is equal to is given by t squared t t now distance between points p and p not is given by square root of t square minus one whole square plus t minus five whole square plus t minus 11 whole square.
01:11
Further solving we get square root of t -raise to power 4 plus 1 minus 2 t -square plus t -square plus 25 minus 10 t plus t -square plus 121 minus 22 t further solving this we get t -raise to power 4.
01:39
Negative of 2 t -square will cancel out for positive of 2 times of 2.
01:43
Of t squared and we are left with negative of 32 times t plus 147.
01:54
Now this is the distance between the points p and p .0.
02:03
Now this distance would be minimum at the point where its derivative would be equal to 0.
02:13
That is where d dash of t is equal to zero.
02:20
Now, this is given by d over d t of square root of t raised to power 4 minus 32 t plus 147, that is 1 over 2 times square root of t raised to power 4 minus 32 t plus 147 times the derivative of inner term, that is 4 t cube minus 32...