Question

hello guys please solve this vector

Answer 1

HELLO FRIEND HERE IS YOUR ANSWER,,,,,,,,

Given,,

$(a \times b).(b \times c)$

This is a clear example of a scalar quadruple product which is very much different from scalar triple products. In this case two cross products are taken into account of dot products or a dot product of two cross products.

Here, "a" variable, "b" variable, "c" variable, "d" variable are the following vectors collected into a 3-D or three dimensional Euclidean space.

Therefore, by using the following evaluate this,,,

(a × b) . (c × d)

=>

[(a).(c)] [(b).(d)] - [(a).(d)][(b).(c)]

So we get,,

=>

(a . c) (b . d) - (a . d) (b . c)

It can also be solved with the help of the determinant.

| a . c a . d |

| b . c b . d |

HOPE IT HELPS YOU AND CLEARS YOUR DOUBTS REGARDING VECTOR DOT PRODUCTS!!!!