The initial and terminal points of a vector are given. Write the vector as a linear combination of the standard unit vectors i and j. Initial Point: (-1, 5) Terminal Point: (9, −8)

Answer 1

the initial point, which I'll call A, can be written in terms of i and j as:

A = -1i + 5j

The terminal point, which I'll call B, can also be written in terms of i and j as:

B = 9i -8j

Now the vector, defined by A and B, which I'll call C is going to be

C = B - A

NOW, it's important to remember that vector subtraction is done on a Component by Component basis.

THAT IS, you get the i component of C by using the i components of A and B and the j component by using the j components of A and B. Otherwise, it's just like regular subtraction.

C = B - A = (9i - 8j) - (-1i + 5j) = (9 - -1)i +(-8 - 5)j = (10)i + (-13)j = 10i -13j