consider and find vectors

Question

A = 2i - 3j

B = 3i + 4j

1) Draw both on an x-y axis

2) Find C = A + B and draw it on that diagram

3) Find D = A - B and draw it on that diagram

Answer 1

Hi Matt D.,

When adding vectors, add the components of like unit vectors:

C = A + B = [ 2i - 3j ] + [ 3i + 4j ] = (2 + 3)i + (-3 + 4)j = 5i + j

To graph the addition of these two vectors, with unit vector ( i ) in the x-direction, and unit vector ( j ) in the y-direction, first draw vector A. On Cartesian coordinates, draw a line from the origin (0, 0) to point (2, -3) and draw an arrow ( > ) at (2, -3). Then draw vector B, from point (2, 3), draw a line 3 units in the positive x-direction and 4 units in the positive y-direction. This line ends at (5, 1), put another arrow at this point. Then draw a line from the origin (0, 0) to point (5, 1) and draw an arrow at the end of this line at (5, 1), this is the addition vector C.

See if you can do C = A - B. [ ai + bj ] - [ ci + dj ] = (a - c)i + (b - d)j

I hope this helps, Joe.