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Vector Addition Using Components

# Vector Addition Using Components - Vector Addition Using...

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Vector Addition Using Components Given two vectors u = ( u 1 , u 2 ) and v = ( v 1 , v 2 ) in the Euclidean plane, the sum is given by: u + v = ( u 1 + v 1 , u 2 + v 2 ) For three-dimensional vectors u = ( u 1 , u 2 , u 3 ) and v = ( v 1 , v 2 , v 3 ) , the formula is almost identical: u + v = ( u 1 + v 1 , u 2 + v 2 , u 3 + v 3 ) In other words, vector addition is just like ordinary addition: component by component. Notice that if you add together two 2-dimensional vectors you must get another 2-dimensional vector as your answer. Addition of 3-dimensional vectors will yield 3-dimensional answers. 2- and 3-dimensional vectors belong to different vector spaces and cannot be added. These same rules apply when we are dealing with scalar multiplication. Scalar Multiplication of Vectors Using Components Given a single vector v = ( v 1 , v 2 ) in the Euclidean plane, and a scalar a (which is a real number), the multiplication of the vector by the scalar is defined as: av = ( av 1 , av 2 ) Similarly, for a 3-dimensional vector v = ( v 1 , v 2 , v 3 ) and a scalar a , the formula for scalar

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Vector Addition Using Components - Vector Addition Using...

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