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

Question

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

Answer 1

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.

.

Answer 2

Our buddy Pythagoras solved this difficulty hundreds of years in the past. He validated that the sq. of the hypotenuse (side opposite the final perspective) is the sum of the squares of the legs (sides adjoining to the final perspective). on your particular difficulty, convert the two lengths to inches. [attempting to multiply and compute roots base-12 is frustrating artwork.] The length of the 0.33 side [hypotenuse] is the sq. root of 26 and a million/12 feet squared plus 40 feet squared.