IIT JEE , AIEEE Forum - Physics , Mechanics - Cross-Product of Vectors

kane

hi guys,plz help me out with this one!!!

is there any way to memorise the results of cross-product of unit vectors.e.g. tell how to know what is i cross j,j cross i, -j cross -i,-k cross -i and similarly other cross products.dot product is too easy.plz do help me out with this one.

Ronaldooo

See,consider a circle in which the elements i,j and k are arranged.Now,go anti clockwise.

   i      ---      k
      \         /
          j
i x j will be k.j x k will be i.kxi will be j.Suppose you have i x k.Then here it will be clockwise and hence a -ve sign will come.i.e,i x k= -j.

Ronaldooo

did you get it??

ravi00

see in xyz x cums 1st similarly i cums 1st in ijk
so we memorize dem

chemicaltester

use series i j k in direction of k
i.e ixj =k
jxk =i
if the series is in opposite direction apply negative signs
jxi =-k

hope u got it

kane

thnxs guys what about j cross i?

srini

Hey,

you are going anticlockwise so same iXj with a negati sig

.

rathin_123

if you write i,j & k in traingle shape like i

k j

and moves to clockwise direction you will get

i * j = k , j * k = i,k * i =j

now if you moves anticlokwise direction

i * k = -j , k * j = -i , j * i = -k

chinmay_saxena01

i totally agreed with rathin

ashish_banga

imagine i along x axis
j along y axis
k along z axis

if u want to find i X j = then curl your right handfingers from x axis to y , this will give u k
similarly i X k = - y axis = -j

Aatish

hey kane........see........

when u move in this manner.......

from i to j to k to i....take it as positive.....if order is opposite take it as negative.....

now remember just one more thing....cross product of any two unit vectors gives the third one.......

for example.........

i x j = k but j x i = -k
j x k = i but k x j = -i
k x i = j but i x k = -j

hope this helps u..........

coolriya

ya..... tats ryt..........
neways.......... the exact1 is..........

Since sin 0 = 0 and sin 90 = 1 and each vector is of unit length, we have
i x i = j x j = k x k = O, (the zero vector).
Also, i x j = k and j x k = i and k x i = j

while j x i = - k and k x j = - i and i x k = - j.
You can see how the various plus and minus signs come by using the right-hand rule for each product.
I've shown this for the case i x j = k :

kane

thnxs a lot everybody for replying!!!!!!

mujtaba4iit

Hey just see the attached image below.
If u take i x j then u get k( see the cyclic motion)
similarly, j x k = i
and, k x i = j.

If u want something in the direction opposite to that of the given direction then the result will have a negative(-) sign.

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