Given the initial (-3,1) and terminal (4,5) points of a vector, how do you write a linear combination of the standard unit vector i and j?
1 Answer
Aug 22, 2017
bb(ul v) = ( (7), (4) ) = << 7, 4 >> = 7bb(ul hat i) + 4bb(ul hat j)
Explanation:
Denote the given coordinates by:
O= (0,0)
A = (-3,1)
B = (4,5)
Then the vector
bb(ul v) = bb(vec(OB)) - bb(vec(OA))
\ \ \ = ( (4), (5) ) - ( (-3), (1) )
\ \ \ = ( (7), (4) )
Alternatively, depending upon the desired notation we can also write:
bb(ul v) = << 7, 4 >> = 7bb(ul hat i) + 4bb(ul hat j)
