Find the curvature and the radius of curvature at the stated...

Transcript

00:01 In this question, we have been given to find the curvature and radius of curvature at the stated point.

00:07 So here we have r of t value as 11 cost t i cap plus 10 sign t j cap and then we can say that it will be plus 10 t k cap.

00:24 So here it can be said that t will be equals to pi over two.

00:29 And so here we can say that r of t value is this.

00:35 So that means r dash t value, that is first differentiation of r of t will be minus 11, sine of t i cap plus 10 cos of t, j cap, minus, and then it will be plus t cap, not minus.

00:54 Minus 3 so it will be plus 10 t now here we can say it will be k cap as well so here at t equals pi over 2 we can say that r double dash t will be equals to minus 11 cost t i cap minus 10 sign t j cap and so we can here write that at t equals pi over 2 r double dash t is equals to minus 11 cost t i cap minus 10 sine t and then here it will be j cap so we can say that here r dash t multiplied r double dash t will be equals to minus 11 i cap plus 10 k cap multiplied minus 10 j cap so this will be equals to 10 i cap sorry 100 i cap plus 110 k cap and hence we can here say that 11 multiplied r dash t multiplied r double dash t is equals to under root of 100 plus 110 and it will be raised to the power 2 for both the terms so it is going to be under root of 22100 and this is going to be equal to 10 under root of 221 because this can be simplified as such so here we can write that 11 r dash t and then here it will be equals to under root of 11 square plus 10 square and this will be equals to under root of 2 to 1.

02:52 So here we can say that curvature x will be equals to 11 r dash t and then it will be multiplied with r double dash t and then here it will be 11 r dash t and then it will be raised to the power 3...

Question

Find the curvature and the radius of curvature at the stated point. r(t) = 11 cos t i + 10 sin t j + 10t k; t = ?/2 Enter the exact, simplified answers. ? = ? =

Question

Find the curvature and the radius of curvature at the stated point. r(t) = 11 cos t i + 10 sin t j + 10t k; t = ?/2 Enter the exact, simplified answers. ? = ? =

Please give Ace some feedback