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What is the projection of (4,4) onto (3,1)?

Bethany Evans

in Mathematics

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Ralph Lopez on January 16, 2019

Let's define the vectors: U = (4.4) V = (3.1) The projection of U to V is proportional to V, The way to calculate it is the following: Project v U = [(U. V) / | V | ^ 2] U. V Where V is the product point of the vectors, | V | ^ 2 is the magnitude of the vector V to the square and all that the operation by V, that is the vector. We have then: U. V Product: U. V = (4,4) * (3,1) U. V = 4 * 3 + 4 * 1 U. V = 12 + 4 U V = 16 Magnitude of the vector V: lVl = root ((3) ^ 2 + (1) ^ 2) lVl = root (9 + 1) lVl = root (10) by Substituting in the formula we have: Project v U = [(16) / (root (10)) ^ 2] (3, 1) Project v U = [16/10] (3, 1) Draft v U = [1.6] (3, 1) Draft v U = [1.6] (3, 1) Draft v U = (4.8, 1.6) Answer: the projection of (4,4) to (3,1) is: Project v U = (4.8, 1.6)


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