# [SOLVED] calc 3 help please

• Jan 27th 2009, 04:33 PM
Legendsn3verdie
i believe this has something to do with crossproducts.
for the part below use:

u= 8i +2j and v = 2i+j-k

find the area of the parallelogram formed by u and v

ok so that was the problem

i started it by trying to find the P, Q, and R.

i got P(8,2,0) Q(2,1,0) and R(0,-1,0)

are the points correct for P Q and R
i m kinda stuck here.
• Jan 27th 2009, 05:13 PM
skeeter
$\displaystyle u \times v$ will give the area ...

Code:

| i  j  k | | 8  2  0 | = 10 | 2  1 -1 |
• Jan 27th 2009, 05:25 PM
Legendsn3verdie
Quote:

Originally Posted by skeeter
$\displaystyle u \times v$ will give the area ...

Code:

| i  j  k | | 8  2  0 | = 10 | 2  1 -1 |

not sure how 10 came out of that.. i see where you got the numbers and how u put them in that chart thing. but i dont see how 10 comes outta that hm.
• Jan 27th 2009, 05:29 PM
skeeter
10 is the determinant of the matrix.
• Jan 27th 2009, 06:10 PM
Legendsn3verdie
Quote:

Originally Posted by skeeter
10 is the determinant of the matrix.

well ty but i still dont get it. i dont want to frustrate you.
• Jan 27th 2009, 06:24 PM
pberardi
The area of a parallelogram is the magnitude of the cross product. So do the cross product, then take the magnitude of that vector.
• Jan 28th 2009, 04:28 AM
skeeter
Quote:

Originally Posted by Legendsn3verdie
well ty but i still dont get it. i dont want to frustrate you.

the magnitude of cross product of the two vectors gives the area of the parallelogram.

when working in rectangular coordinate systems, the cross product of vectors a and b given by

http://emweb.unl.edu/math/mathweb/vectors/Image550.gif

can be evaluated using the rule

http://emweb.unl.edu/math/mathweb/vectors/Image551.gif
• Jan 28th 2009, 09:30 AM
Legendsn3verdie
Quote:

Originally Posted by skeeter
the magnitude of cross product of the two vectors gives the area of the parallelogram.

when working in rectangular coordinate systems, the cross product of vectors a and b given by

http://emweb.unl.edu/math/mathweb/vectors/Image550.gif

can be evaluated using the rule

http://emweb.unl.edu/math/mathweb/vectors/Image551.gif

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