Calculate the angle between: a = (10, 5)^T and b = (8, 12)^T

The lengths are: | a | = √125, | b | = √208.

The dot product is:

(10, 5)^T / √125 · (8, 12)^T / √208 = (10*8 + 5*12) / ( √125 √208)

= 140 / ( √125 √208) = 140 / √(125*208) = 140 / √26000 = 0.86824

so the angle is: arc cos ( 0.86824 ) = 29.745°

End of the Chapter

This chapter had quite a bit of numerical computation in it. Be careful that you did not loose sight of the important points:

You have reached the end of the chapter.