so far for this querstion i simplified the line to y=-3/4x + 3 and identified the intersect of (4,0) and (0,3)

https://www.desmos.com/calculator/i0vbehvizi

knowing that the magnitude is 5/2 i'm guessing the solve would be to form a triangle with intersects, the line and point B which would be 5/2 away from 0

but i don't know how to find the point B using the magnitude, please help thanks

YEEEEEET Feb 24, 2019

#3**+3 **

\(\text{why not just do}\\ p=\left(x, \dfrac{12-3x}{4}\right)\\ |p|^2 =\dfrac{25 x^2}{16}-\dfrac{9 x}{2}+9= \dfrac{25}{4}\\ 25x^2 - 72x+144= 100\\ 25x^2 - 72x+44 = 0 \\ x = \dfrac{22}{25},~2\\ \vec{OB} = \dfrac{22}{25}\hat{i} + \dfrac{117}{50}\hat{j}\\ \vec{OB} = 2\hat{i} + \dfrac 3 2 \hat{j}\)

.Rom Feb 24, 2019