class_2(vector_alge)

class_2(vector_alge) - Vector Multiplication Scalar (or...

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Vector Multiplication AB x x y y z z A B A B cos A B A B A B A B = θ = + + r r r r r r Scalar (or dot) product Rules: Commutative: A B B A = r r r r Distributive: Find magnitude of a vector: A (B C) A B A C + = + r r r r r r r 2 A A A = r r r
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Some simple identities x y a a = x z a a = z y a a = x x a a = y y a a = z z a a = 0 0 0 1 1 1
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Example 1.4 AB A B A B cos = θ r r r r Given vectors A =3 a x +4 a y +1 a z and B =2 a y -5 a z , find the angle between A and B Solution: The angle can be found using dot product between A and B AB A B cos A B B θ = r r r r x x y y z z A B A B A B A B 3 0 4 2 1 ( 5) 3 = + + = + + - = r r 2 2 2 x y z A A A A 26 = + + = r 2 2 2 x y z B B B B 29 = + + = r AB A B cos 0.1092 A B B θ = = r r r r o AB 83.73 θ =
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AB n A B A B sin a = θ r r r r r Vector (or cross) product n a r Is a unit vector normal to the plane containing vector A and B. Its direction is found using right thumb rule. A
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class_2(vector_alge) - Vector Multiplication Scalar (or...

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