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#?

1 Answer
Douglas K.
Dec 31, 2017

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#

Explanation:

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")#

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