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)#
