Evaluate . ; S is the part of the torus with vector representation , , .
C)0

Question

Evaluate  .  ; S is the part of the torus with vector representation  ,  ,  .
C)0

Quizplus · Accepted Answer

We first subtract the two given vectors to get the vector representation of the line passing through their endpoints, which is (0, 0, 0, -1). Next, we take the cross product of this line and the vector representation of S to get (0, 0, 0, 1), which is a vector with positive fourth component. This means that S lies on the positive side of the plane passing through the origin and perpendicular to the line, so it does not intersect the torus. Therefore, the answer is (D) 11eaa3e5_54ba_600d_9f8f_41186ec66479_TB5971_11, the choice representing no intersection.