By Andy Ruina, Rudra Pratap
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15: ˆ AB is a unit vector along AB. So now we need to find λ ˆ AB . We can easily where λ ˆ AB if we know vector AB. Let us denote vector AB by r AB (sometimes we find λ will also write it as r B/A to represent the position of B with respect to A as a vector). Then, ˆ AB = r AB . 5 m A r AB 1m rA rB To find r AB , we note that (see Fig. 8 mk. 16: r AB = r B − r A . 2 m where r A and r B are the position vectors of point A and point B respectively. Hence, r B/A B ˆ AB (100 N) λ ˆ −29 Nˆı + 57 Nˆ − 77 Nk.
Components times unit base vectors. F = Fx ıˆ + Fy ˆ or F = Fx ıˆ + Fy ˆ + Fz kˆ in three dimensions. One way to think of this sum is to realize that F x = Fx ıˆ, ˆ F y = Fy ˆ and F z = Fz k. Components times rotated unit base vectors. F = Fx i + Fy j or F = Fx i + Fy j + Fz k in three dimensions. Here the base vectors marked with primes, i , j and k , are unit vectors parallel to some mutually orthogonal x , y , and z axes. These x , y , and z axes may be crooked in relation to the x, y, and z axis.
5b shows that r B/A = r B − r A which rolls off the tongue easily and makes the concept of relative position easier to remember. 1 1 For the first 7 chapters of this book you can just translate ‘relative to’ to mean ‘minus’ as in english. ’ means what is Rudra’s wealth minus Andy’s wealth? What is the position of B relative to A? It is the position of B minus the position of A. 12 CHAPTER 2. 6: Multiplying a vector by a scalar stretches it. stretch) Naturally enough 2F means F + F (see fig. 6) and 127A means A added to itself 127 times.