Chapter 9 - Polar Coordinates; Vectors - 9.5 The Dot Product - 9.5 Assess Your Understanding - Page 615: 10

a)$=0.$ b)$90^\circ$. c)orthogonal.

By definition the dot product of 2 vector $ai+bj$ and $ci+dj$ is: $(ai+bj)(ci+dj)=ac+bd.$ If this product is 0, then the vectors are orthogonal (perpendicular) and hence the enclosed angle is $90^\circ.$ a)$v\cdot w=(i+j)(-i+j)=1\cdot(-1)+1\cdot1=0.$ b)From above the enclosed angle is:$90^\circ$. c)From above they are orthogonal.