Question

Find the area of the parallelogram with the defining vectors
i) a=( 4,-5) and b= (7,2)
ii) a= (4,-5,3) and b= (7,2,-4)

Answer 1

subtract one vector from the other to get it to the origin; is my first thought

Answer 2

but my first thought aint always too good :)

Answer 3

maybe better idea.

magnitude of b * height; where height is the "a"sin(a)

Answer 4

the determinate of the vector matrix of the first one would be good, but not work out to well for the second

Answer 5

i can recall the dot product stuff for cos(t) but never for sin(t) for some reason

Answer 6

Thank you!!

Answer 7

The cross product a × b is defined as a vector c that is perpendicular to both a and b, with a direction given by the right-hand rule and a magnitude equal to the area of the parallelogram that the vectors span. from the wiki i think

Answer 8

so |axb| seems to be the area of the parallelogram if im reading this right

Answer 9

now i gotta recall how to cross a 2component vector

Answer 10

3 components i can do :)

Answer 11

ii) a= (4 -5 3)
and b= (7 2 -4)
---------------
x = 20-6 = 14
y=-(-16-21) = 37
z = 8+35 = 43

sqre them add them and sqrt them for magnitude; might wanna use a calcultor :)

Answer 12

http://www.wolframalpha.com/input/?i=sqrt%2814%5E2%2B37%5E2%2B43%5E2%29

58.5 thereabouts?

Answer 13

cross was good; i can wolf the other one for simplicities sake too

Answer 14

determinant of the vector matrix on 1 is 43, with any luck i recalled that stuff right

Answer 15

woowww thank you soo soo much!! :)

Answer 16

do we know if i was right? lol