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Area between x=g(y) and y Axis

Calculate the...

Question

Calculate the scalar product of the following vectors.
Two points A and B are given in the rectangular Cartesian system of coordinates Oxy on the curve $y = 6 / x,$ the points being such that $- - \to O A \cdot i = - 2 a n d - - \to O B \cdot i = 3,$ where i is a unit vector of the Ox axis. Find the length of the vector $- -- \to 2 O A + - -- \to 3 O B .$

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Solution

let $A = (x_{1}, y_{1})$ and $B = (x_{2}, y_{2})$
given $\to O A . i = - 2 ⟹ x_{1} = - 2$ and $\to O B . i = - 3 ⟹ x_{2} = 3$

$A, B$ are points on the curve $y = \frac{6}{x}$ . Using this to find the ordinates of A and B.

$y_{1} = \frac{6}{x_{1}} = - 3$ and $y_{2} = \frac{6}{x_{2}} = 2$

$2 \to O A + 3 \to O B = 2 (- 2 i - 3 j) + 3 (3 i + 2 j) = 5 i + 0 j$
The length of this vector is given by $\sqrt{5^{2} + 0^{2}} = 5$

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