Two vectors have their tails connected and their lengths fixed. If the angle between them is now varied,.....?

Two vectors have their tails connected and their lengths fixed. If the angle between them is now varied,.....


which of the following is true?





i. The magnitude of the dot product is minimized when the vectors are perpendicular.


ii The magnitude of the dot product is maximized when they are perpendicular.


iii Each will always have a component lying along the other.





a.) i only


b.) ii only


c.) iii only


d.) i and ii only


e.) i and iii only


f.) i, ii, and iii

Two vectors have their tails connected and their lengths fixed. If the angle between them is now varied,.....?
A





Dot product = |a| * |b| * cos(angle)


if the angle=90; cos(90)=0, so that is as minimum as it gets.





iii is false, because at 90 degrees the component of one versus the other is 0 (so at that point the don't 'always' have one lying along the other.





.