Determine whether the following trajectory lies on either a circle in R? or a sphere in...

 

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Determine whether the following trajectory lies on either a circle in R? or a sphere in R° centered at the origin. If so, find the radius of the circle or sphere, and show that the position vector and the velocity vector are everywhere orthogonal. r(t) = (12 sin 21, 12 cos 21), for 0stsa Determine whether the following trajectory lies on either a circle in R? or a sphere in R centered at the origin. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. The trajectory lies on a sphere with radius . (Simplify your answer.) B. The trajectory lies on a circle with radius 12. (Simplify your answer.) The trajectory does not lie on a circle or a sphere. Show that the position vector and the velocity vector are everywhere orthogonal. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. Since r•v= (O (24 cos (21) + (12 cos 2t)| (Type exact answers.) for 0stsz, the position vector r and velocity vector v are orthogonal. B. Since rxv= 12 cos 21) x (24 cos (21) = ( (Type exact answers.) for 0stsr, the position vector r and velocity vector v are orthogonal. O C. Since rxv .0) x (24,)= (Type integers or decimals.) , the position vector r and velocity vector v are orthogonal. OD. Since r•v= (D 24) +(12)(D = , the position vector rand velocity vector v are orthogonal. (Type integers or decimals.) O E. The trajectory does not lie on a circle or a sphere. Determine whether the following trajectory lies on either a circle in R? or a sphere in R° centered at the origin. If so, find the radius of the circle or sphere, and show that the position vector and the velocity vector are everywhere orthogonal. r(t) = (12 sin 21, 12 cos 21), for 0stsa Determine whether the following trajectory lies on either a circle in R? or a sphere in R centered at the origin. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. The trajectory lies on a sphere with radius . (Simplify your answer.) B. The trajectory lies on a circle with radius 12. (Simplify your answer.) The trajectory does not lie on a circle or a sphere. Show that the position vector and the velocity vector are everywhere orthogonal. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. Since r•v= (O (24 cos (21) + (12 cos 2t)| (Type exact answers.) for 0stsz, the position vector r and velocity vector v are orthogonal. B. Since rxv= 12 cos 21) x (24 cos (21) = ( (Type exact answers.) for 0stsr, the position vector r and velocity vector v are orthogonal. O C. Since rxv .0) x (24,)= (Type integers or decimals.) , the position vector r and velocity vector v are orthogonal. OD. Since r•v= (D 24) +(12)(D = , the position vector rand velocity vector v are orthogonal. (Type integers or decimals.) O E. The trajectory does not lie on a circle or a sphere.