# 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)#