By William J. O'Neil
Presents confirmed, easy-to-apply thoughts for construction a ecocnomic portfolio. Cuts in the course of the static of traditional knowledge with a clean array of commonsense innovations that assist you adequately gauge the industry, purchase and promote on the correct second, and effectively deal with your portfolio.
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Extra resources for 24 Essential Lessons for Investment Success: Learn the Most Important Investment Techniques from the Founder of Investor's Business Daily
Similarly the x and y components of MC are the moments about the ıˆ and ˆ axis through C. So at least the components of MC have intuitive meaning. They are the moments around the x, y, and z axes respectively. Starting with this moment-about-the-coordinate-axes interpretation of the moment vector, each of the three components can be deduced graphically by the moves shown in fig. 30. The force is first broken into components. The components are then moved along their lines of action to the coordinate planes.
8ˆ) 20 CHAPTER 2. 8 Position vector from the origin: In the x yz coordinate system, a particle is located at the coordinate (3m, 2m, 1m). Find the position vector of the particle. Solution The position vector of the particle at P is a vector drawn from the origin of the coordinate system to the position P of the particle. See Fig. 13. We can write this vector as z r 1m x y (3m,2m,1m) or 3m rP = rP = (3 m)ˆı + (2 m)ˆ + (1 m)kˆ ˆ m. 13: The position vector of the particle is a vector drawn from the origin of the coordinate system to the position of the particle.
A]x1 x2 = [A1 , A2 ]), the cross product is A × B = (A1 B2 − B2 A1 )eˆ3 . ” Example: Given that A = 1ˆı + 2ˆ and B = 10ˆı + 20ˆ then A × B = (1 · 20 − 2 · 10)kˆ = 0kˆ = 0. ✷ y F ry For vectors with just a few components it is often most convenient to use the distributive rule directly. 6ˆı ) + (7ˆı ) × (10ˆ) = 0 + 70kˆ = 70k. ✷ rx y Fx You have several options for calculating the 2D cross product. Which you choose depends on taste and convenience. You can use the geometric definition directly, the first times the perpendicular part of the second (distance times perpendicular component of force), the second times the perpendicular part of the first (lever arm times the force), components, or break each of the vectors into a sum of vectors and use the distributive rule.