if the diagonals of a parallelogram are 3i^ + j^ -2K^ and i^ -3j^ +4K^ then how can we find the area.

Question

if the diagonals of a parallelogram are 3i^ + j^ -2K^    and i^ -3j^ +4K^ then how can we find the area.

praxer · Answer

@Callisto please help me..

callisto · Answer

Suppose we have to vectors a and b, which form the parallelogram. Since the given vectors are the diagonal of the parallelogram, a + b = <3, 1, -2> a - b = <1, -3, 4> Solve for a and b. With a and b, I think you can find the area of parallelogram using cross product.

praxer · Answer

@Loser66  can u hlp me with this please..

loser66 · Answer

what grade are you? Do you know cross product?

praxer · Answer

i know cross product but i didn't get the explanation above... So, i am asking

loser66 · Answer

ok, just follow him, and ....we find the meaning of the logic then, Ok?

praxer · Answer

ok.

loser66 · Answer

get a, b from his equation first, what do you have?

praxer · Answer

ok a+b is<4,-2,2> a-b is <2,4,-6> then?

praxer · Answer

ok i get it he was saying like a+b to be the sides which add to give one diagonal and a-b to be the other is it so?

loser66 · Answer

let a =(a1,a2,a3)
    b =(b1,b2,b3)
a+b = (a1+b1, a2+b2,a3+b3) = (4,-2,2) 
a -b = (a1-b1,a2-b2,a3-b3)= (2,4,-6)
so, you have a1+b1= 4 
                        a1-b1 = 2
solve it, you have a1=3,b1= 1
got me so far?? do the same to get a2, b2, and a3 b3

praxer · Answer

is it like a+b = <3,1,-2> a-b =< 1,-3,4> now a+b+a-b = 2a = < 4, -2,2> now a=< 2,-1,1> b=<1,2,-3> now from cross product rest can be done. Is this correct???? @Loser66

loser66 · Answer

wow, impressive, you got it!!! |dw:1386773918848:dw|

praxer · Answer

Sorry for the annoyance :). Anyways thank u :)

praxer · Answer

ohk i will

loser66 · Answer

oh, you are right, my bad, I type the wrong numbers. hehehe.. sorry.

loser66 · Answer

you are on the right track and you understand why you do so, right?

praxer · Answer

Yup, i understood it..

loser66 · Answer

good luck

praxer · Answer

Thank you ! 
:)

loser66 · Answer

np

praxer · Answer

I suppose u wont require a good luck, you are so good in mathematics... :)

loser66 · Answer

nope, I always failed at the silly mistake which ruins all my stuff.

praxer · Answer

Talent matters. At least you can proceed. But i am sicked of maths.. Anyways i shall practice from 2day onwards.