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  • 4 years ago

Searched google for a half hour and couldn't find anything that helpful. The best I could find was http://www.math.jhu.edu/~vlorman/32.pdf Given vectors a and b, do teh equations x CROSS a = b and x DOT a = ||a|| determine a unique vector x? Argue both geometrically and analytically. Any help is appreciated.

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  1. phi
    • 4 years ago
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    i think we can use x dot a = |x| |a| cos A and | x cross a | = |x| |a| sin A to show we get x to a sign (i.e. two possible directions)

  2. phi
    • 4 years ago
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    if vectors a and b are not orthogonal, then there is no x such that x cross a = b (because b must be orthogonal to both x and a) if a and b are not zero and orthogonal, we get a unique x x will form an angle A= atan( |b|/|a|) with vector a, and have length= |a| tan A

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