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Applications of Dot Product

Calculate the...

Question

Calculate the scalar product of the following vectors.
Given two vectors $a = {1, - 1, 3} a n d b = {3, - 5, 6} .$ Calculate $P r o j_{(a + b)} (2 a - b) .$

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Solution

Given $a = (1, - 1, 3), b = (3, - 5, 6)$
$2 a - b = (- 1, 3, 0)$
$a + b = (4, - 6, 9)$
$P r o j_{(a + b)}^{(2 a - b)} = \frac{(2 a - b) . (a + b)}{| a + b |} = - \frac{22}{\sqrt{133}}$

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