If s is scalar, s = s Proving iff statement: two vectors v+w are orthogonal iff v w = 0. 1. Assume v+w are orthogonal. Then angle between them, , is 2. So v w = v w cos 2 = = 0. w cos = 0. Since v+w are nonzero, v ie. the vectors are orthogonal. 0 an
1. A vector function is a function that assigns to each x a vector r. Just like a regular function assigns a point. 2. A vector function can be represented by a space curve. A space curve is just a plane curve in 3 dimensions. (A vector function can
f F t = f F t = f t F t (scalar function times vector function) F x G t =F t xG t F G t = blah blah blah.all operations pretty much work You can even stick limits on both sides. Continuity is defined the same way as before.
Thm 14.2.3: If the nonzer
Kepler's Laws: 1. A planet revolves around the sun in an elliptical orbit with the sun at one focus. 2. A line joining the sun to a planet sweeps out equal areas in equal times. 3. The square of the period of revolution of a planet is proportional to
15.1 Functions of Several Variables We write a function of 2 variables as f x, y = z. Ex. Let f x, y = 9 x2 4 y2 f 2, 1 = 1 Domain: All x, y R such that x2 4 y2 9 (all points on or inside the ellipse x2 4 y2 = 9). Operations of functions with 2 varia
Functions of Several Variables
You can use level curves or contour curves to graph a function of 3 variables. Just set z = C, a constant. Pick several values of C and visualize the curve from these level curves. If z = C intersects z x, y , the conto