Question

what is the geometric significance of the dot and cross products?

Answer 1

DOT PRODUCT (A.B)
CROSS PRODUCT (A X B)

Answer 2

CROSS PRODUCT GIVES YOU A VECTOR AS A RESULT BUT DOT PRODUCT WILL GIVE YOU A VALUE

Answer 3

CROSS PRODUCT HAS DIRECTION AND MAGNITUDE WHEREAS DOT PRODUCT DOES GIVE YOU ONLY THE MAGNITUDE

Answer 4

ok, i know how to calculate the 2, but my prof has stated that we need to know the geometric significance and I do not understand that

Answer 5

dot product is multiplication of parts of two vector that are parrellel.

cross product multiplication of parts of two vector that are perpendicular

Answer 6

cross product find us area of parellellagram

Answer 7

ah ha! I believe that is what I needed, thank you. :)

Answer 8

a.b
The dot product has the geometric interpretation as the length of the projection of a onto the unit vector b cap when the two vectors are placed so that their tails coincide.
axb
The magnitude of the cross product can be interpreted as the positive area of the parallelogram having a and b as sides

Answer 9

that also helps, thank you.