Given the initial $(-1, -5)$ and terminal $(2,3)$ points of a vector, how do you write a linear combination of the standard unit vector $hati$ and $hatj$ ?

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Answer 1 · 2017-12-31T14:43:59

When given an initial point, $(x_1,y_1)$ , and a terminal point $(x_2,y_2)$ , the linear combination of unit vectors is as follows:

$vecV= (x_2-x_1)hati+(y_2-y_1)hatj$

Extending the answer to the given initial point, $(-1,5)$ , and terminal point, $(2,3)$ :

$vecV = (2- -1)hati+(3- -5)hatj$

The - - becomes +:

$vecV = (2+1)hati+(3+5)hatj$

$vecV = 3hati+8hatj color(red)(larr " Answer")$

Given the initial (-1, -5)(-1, -5) and terminal (2,3)(2,3) points of a vector, how do you write a linear combination of the standard unit vector hatihati and hatjhatj?