Question

143.29 Determine whether the following trajectory los on either a circle in RP or a sphere in centered at the origin. If so, find the radius of the circle or share and show that the position vector and the valoaty vector are everywhere orthogow () = 7cos 21,7 in 21). for Osts Determine whether the following sectory to on other a cirde ha or a sphere in centered at the origin Select the corect choice below and, if necessary, fi in the answer box to compito your choice. OA. The trajectory los on a sphere with radius (Simplify your answer 8. The trajectory les on a circle with radius 7. (Simplify your answer.) c. The trajectory does nolle on acide or a sphere Show that the position vector and the velocity vector are everywhere orthogonal. Select the correct choice below and, if necessary to in the war box to complete your choice O A Sincer-v-De-14 in cam+sin 2) - Osts, the position vector and velocity vector are orthogonal Type ead answers) OB. Sicer (0) the position vector and velocity vector are orthogonal Types of decimas OC. Since xv712) { – 14 sin (21)- tor Osts, the position vector and velocity vector ve ortogonal Type aanswers) ODT 17) (0)). the portion vector and velocity vector orthogonal (Type Wiegers or decima OL The rectory does not to a circle or a here Click to select and enter your and then click Check Answer All parts showing 0 * G Search or type URL esc & M 8 9 0 NE 5 6 P

Answer 1

Ans ? We have rect) =< 7 cosat, 7 sinat> for ostea Flere, nit)=7 cosat, ylt) = 7 sinat and Z(+)=0 i.e relt) is a-dimensional (R²) So, it is a 2-D object and hence can't be a sphere which is 3.) If the parametric equation represents circle, we can write it in the furen of standard circole equation, (n-a)²+(4-6) 2= r² where centre is (a, b) and radius is é. رندارد - (act)) ?+ (yet)) ? 49 ces²2t + 4a Sinzat 249 (ces at + sin?t) = 49=72 sol relt) re preesents a circle with centree at (0,0) and radius r = 7 '. B. The trajectorey lies on a circle with radius 7.

we have the position recture: 7(+)= <teosat, 7 sinat> for ostsa And rectar Wet) = dt velocity o (RPH)) 1) at <7 osat, 7 sinat) =< d t (7 cosat), at 17 Sin2t)) =<-14 sinat, 14 casad> So, we have ♡ (t) = <-14 Sinat, 14 osat) How, fct). ♡ (t) =<7a52t, 7 sinat). <-14 sinat, 14 cosat osat) =(7 cosat) (-14 sinat) + (7 sinat) (14 osat) q8 sinat.cosat taqsinat. cosat is zero since the dot preeduct of re (t) and > (4) the position vectore and the velocity vector are wrethogonal to each other A. Since reva (7 cosat) (-14 sinat) + (7 Sinat) (14 cosat) 0 for ostsa, the position vectorisé and the relocity rectore' v' are orthogonal.