Offer is not valid on tax-exempt trusts, 401(k) accounts, Keogh plans, profit sharing plans, money purchase plans, accounts managed by TD Ameritrade Investment Management, LLC, TD Ameritrade Institutional accounts, or current TD Ameritrade accounts. This is because if q = 90 degrees above, then a To receive 600 bonus, account must be funded with 250,000 or more. b = | a| | b | cos q, where q is the angle between a and bĪn important fact is that two vectors are perpendicular (orthogonal) if and only if their dot product is zero.We can use the scalar product to find the angle between two vectors, thanks to the following formula:Ī If a = i + 4 j - 2 k and b = 2 i + 4 j + 6 k, then a We write the scalar product of two vectors a and b as a Note that this is a scalar number (it is not a vector). So multiply the coefficients of i together, the coefficients of j together and the coefficients of k together and add them all up. Ī i + b j + c k and d i + e j + f k, then their scalar (or dot) product is: ad + be + fc. The position vector of the intersection point is therefore given by putting t = -2/3 or s = 5/3 into one of the above equations. When they intersect, we can set the equations equal to one another: If we are given the vector equations of two different lines, we can work out where the lines cross from their equations.įind where the lines with equations r = i + j + t (3 i - j) and r = - i + s ( j) intersect. This means that for any value of t, the point r is a point on the line. The vector equation of a line passing through the point a and in the direction d is: Notice that = - a + b = b - a because you can get from A to B by going from A to O and then going from O to B. You can draw in the origin wherever you want. Position vectors are vectors giving the position of a point, relative to a fixed point (the origin).įor example, the points A, B and C are the vertices of a triangle, with position vectors a, b and c respectively:
We denote the magnitude of the vector a by | a | VectorVest gives you ANSWERS, not just data. VectorVest is the only stock analysis and portfolio management system that analyzes, ranks and graphs over 18,000 stocks each day for value, safety and timing and gives a clear buy, sell or hold rating on every stock every day. The magnitude of a i + b j = √(a 2 + b 2) that helps you make money in the stock market. The magnitude of a vector can be found using Pythagoras's theorem. Writing vectors in this form can make working with vectors easier. The unit vector in the direction of the x-axis is i, the unit vector in the direction of the y-axis is j and the unit vector in the direction of the z-axis is k. There are three important unit vectors which are commonly used and these are the vectors in the direction of the x, y and z-axes. Examples include speed, time and distance.Ī unit vector is a vector which has a magnitude of 1. A scalar quantity is has only magnitude (so the direction is not important). Acceleration, velocity, force and displacement are all examples of vector quantities. A vector quantity has both magnitude and direction.
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