00:01
Hi, in this question we are given with r of t to be equals to 3t minus 1, 3 times e raised 2 par minus 3t, 3 times e raised 2 par minus 4t.
00:13
And we need to find the line tangent to rt at t is equal to 3.
00:18
At t is equal to 3, that means the line must pass through r of 3 that is equals to 8, 3 times e raised 2 per minus 9, 3 times e r s 2 per minus 12.
00:33
And the derivative of the path r dash t would be equals to 3 minus 9 e raised 2 per minus 3 t minus 12 e r raised 2 per minus 4 t.
00:52
R dash 3 would be equals to 3 minus 9 e raised 2 per minus 9 minus 12, e -raise 2 par minus 12.
01:07
Now, finding the equation of the tangent line, that would be l of t, and this would be equals to r at 3 plus t minus 3 times r -dash 3.
01:28
Or we can write this to be equals to r3, that is 8 i cap.
01:37
Plus 3 e rase to per minus 9 j cap plus 3 e r .m...