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Published byOswin Benson Modified over 9 years ago
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The Vector Product
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Remember that the scalar product is a number, not a vector Using the vector product to multiply two vectors, will leave the answer in form of a vector. The good news is that you will not have to remember this formula
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Rearrange the vectors as follows The vector product
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One very important property of the vector product is: It will always be perpendicular to both vectors, a and b
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Note that any combination of coordinates could have been used to find the normal vector, as well as any coordinates could have been used to find a value of k.
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Angle between two planes
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Point of intersection of a line and a plane The points of intersection can be found when the equation of the line is expressed in parametric form.
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The angle between a line and a plane Note t hat we are using sin
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Line intersection of two planes If two planes intersect, they intersect in a line. The parametric form of the line can be found as follows Using the parametric form, the equation of the line is
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The shortest distance between the point and the line is therefore 7 units
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The shortest distance between the point and the plane is therefore 15 units
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