Question

what is the value of B vector× B vector​

Answer 1

Answer:

We know that, cross(vector) product of two vectors is a third vector whose magnitude is given by the product of magnitude of given vectors multiplied by sin ratio of the smaller angle between them. In your case, given two vectors are the same, i.e., A and hence, they are equal in magnitude and angle between them is 0°.

Answer 2

Answer:

We know from scalar triple product, that for vectors A, B, and C,

A . ( B × C) = B . ( C × A) = C . ( A× B) = (A×B) . C

In our question

( A + B ) . ( A × B ) = A. ( A× B) + B . ( A × B)

Now

A. ( A× B) = B. ( A×A)= 0

and

B . ( A ×B ) = A. ( B× B)= 0

Therefore,

( A +B ) . ( A × B ) = 0 +0= 0

The dot product of the sum of two Vectors with the cross products of the same two vector is zero and a scalar.

We can understand the answer as below. The sum of two vectors A and B is a vector in the plane defined by A and B. Whereas A×B is a vector which is perpendicular to the plane of vectors A and B. The dot product of two vectors one in the plane of vectors A,B and the other perpendicular to the plane is zero. Furthermore being a dot product it is a scalar.