Question

A=i+j The value of
B=i-j (A+B).(A-B) It is simple but i don't know where i am making a mistake

Answer 1

(A+B)(A-B) = A.A - A.B + B.A - B.B = A.A - B.B = |A|^2 - |B|^2

Answer 2

This is one method in which you will only have to calculate the magnitude of each vector and you would get the answer :)

Answer 3

Another method is to calculate (A+B) and (A-B) and then evaluate the dot product

Answer 4

Now which one did you use ?

Answer 5

I did
A+B =2i
A-B=2j

so 2i*2j = 4 ?

Answer 6

Actually it is not * it is dot product

Answer 7

\[\large{\boxed{* \ne \cdot}}\]

Answer 8

(A+B)=2i+0j
(A-B)=0i+2j

Answer 9

yeah .

Answer 10

In vector algebra there are generally two types of products - dot product (scalar product) or cross product (vector product).

Answer 11

If:

\[\large{{\bf{U}} = U_x \hat{i} + U_y \hat{j} + U_z \hat{k}}\]

\[\large{{\bf{V}} = V_x \hat{i} + V_y \hat{j} + V_z \hat{k}}\]

Then:

\[\large{{\bf{U}}\cdot {\bf{V}} = U_x V_x + U_y V_y + U_z V_z}\]

Answer 12

This is called dot product ^^^

(The one the problem asks for)

Answer 13

yess , for the other one we have to make a matrix

Answer 14

Yup that one is vector product

Answer 15

Now that you know how to calculate dot product. Can you find out the answer ?

Answer 16

yes sure wait :)

Answer 17

Take your time :)

Answer 18

<2i+0j>.<0i+2j>

0+4-0+0 = 4

Answer 19

How did you get this 4 ?

Answer 20

Why ?

Answer 21

right**

Answer 22

See:

\[\large{\vec{A}\cdot \vec{B} = |\vec{A}||\vec{B}|\cos{\theta}}\]

For \(\large{\hat{i},~\hat{j}}\), \(\theta\) is 90 degrees, so dot product is zero.

Answer 23

So i.j = 0 not 1

Answer 24

Thus, answer must be 0 not 4.

Answer 25

yes 0 is the answer

Answer 26

So do you understand it ?

Answer 27

Yes really got it
(2i).(2j) =0 as i.j=0

Answer 28

Very good :)