MATH 23A Study Guide - Midterm Guide: Parallelepiped, Right-Hand Rule, Fxx
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Se(cid:272)tio(cid:374) (cid:1005). (cid:1005): ve(cid:272)tors i(cid:374) t(cid:449)o a(cid:374)d three di(cid:373)e(cid:374)sio(cid:374)al spa(cid:272)e. Se(cid:272)tio(cid:374) (cid:1005). (cid:1006): the i(cid:374)(cid:374)er produ(cid:272)t, le(cid:374)gth a(cid:374)d. Se(cid:272)tio(cid:374) (cid:1005). (cid:1007): matri(cid:272)es, deter(cid:373)i(cid:374)a(cid:374)ts, a(cid:374)d the cross produ(cid:272)t. Se(cid:272)tio(cid:374) (cid:1006). (cid:1005): the geo(cid:373)etry of real-valued fu(cid:374)(cid:272)tio(cid:374)s. Se(cid:272)tio(cid:374) (cid:1006). (cid:1008): i(cid:374)trodu(cid:272)tio(cid:374) to paths a(cid:374)d cur(cid:448)es. Section 1. 1: vectors in two and three dimensional space. Geometrically: directed line segments (arrows with speci c lengths) If the tail is at the origin and the head is at the point (x, y, z) the vector is represented by hx, y, zi. The book does not follow hi notation and uses ( ). The vector for the point p ( 1, 3, 4) to q(2, 1, 2) is. P q =d2 ( 1), ( 1) 3, 2 4e = h3, 4, 2i called displacement vector from p to q. In general vector from (x1, y1, z1) to (x2, y2, z2) is hx2 x1, y2 y1, z2 z1i.
