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05Scalar Product and Angles Between Lines

05Scalar Product and Angles Between Lines - SCALAR PRODUCT...

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S CALAR P RODUCT AND A NGLES B ETWEEN V ECTORS The scalar product (dot product) of two vectors is: θ cos b a b a = where θ is the angle between the two vectors if they are drawn from the same point. The angle may be acute, right, or obtuse. The result of a scalar (dot) product is a scalar quantity. The scalar product is most often used to find the angle between two vectors – therefore the equation can be rewritten as: b a b a = θ cos To find the product b a , assume that = 2 1 a a a and = 2 1 b b b . Then the scalar product is 2 2 1 1 b a b a + . (Note that this is like multiplying matrices). The scalar product for vectors in three or more dimensions is similar. Ex . Find the magnitudes and scalar products for each pair of vectors. Hence, find the angle between each pair of vectors. a) j i 3 + - and j i 2 + - b) - 4 5 0 and - - - 3 1 5
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If two vectors are perpendicular, what should the scalar product be equal to? If two vectors are parallel, what should the scalar product be equal to?
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