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7 Cards in this Set
- Front
- Back
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Work |
work = ||Proj of F onto direction||*distance work was done on amount of force exerted times distance it is being exerted |
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How to find proj of u onto v when the angle between then is given |
- in this case u is the hypotenuse and v is the side adjacent to the known angle - simply solve for the length of u (u is no longer the vector stated above, it is the side of the triangle in the same direction as the vector u - you now know the magnitude of proj of u onto v, so simply find the unit vector of u and multiply it by your magnitude. - you now have the full vector proj of u onto v |
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How to find proj of u onto v with just the vectors themselves |
- use the formula proj of u onto v = [(u*v)/(||v||^2)] * v |
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how to find the angle between two vectors using the dot product What is the alternative form of the dot product |
- cos(theta) = (u*v)/(||u||*||v||) thus arccos((u*v)/(||u||*||v||)) = theta - (u*v) = ||u||*||v||*cos(theta) |
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how to find direction cosines of a vector |
- find the unit vector - take the arccos of each i, j and k |
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Given 2 vectors (u and v), find a vector that is orthogonal to one of them |
- find the proj of u onto v - subtract that from the vector you want it to be orthogonal to |
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What is the formula for the cross product of two vectors using an angle and the magnitude of two vectors |
||u||*||v||*sin(theta) |
