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 $\overrightarrow{OA}\cdot i=-2and\overrightarrow{OB}\cdot i=3,$ where i is a unit vector of the Ox axis. Find the length of the vector $\overrightarrow{2OA}+\overrightarrow{3OB}.$

Answer 1

let $A=(x_1,y_1)$ and $B=(x_2,y_2)$

given $\overrightarrow{OA}.i=-2⟹x_1=-2$ and $\overrightarrow{OB}.i=-3⟹x_2=3$

$A,B$ 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 $y_2=\frac{6}{x_2}=2$

$2\overrightarrow{OA}+3\overrightarrow{OB}=2(-2i-3j)+3(3i+2j)=5i+0j$

The length of this vector is given by $\sqrt{5^2+0^2}=5$