Question

prove that the whole square of A vector × B vector= A²B²-(A vector . B vector)?​

Answer 1

$\huge \underline \green{\sf{ Answer :- }}$

Cross product of two vectors gives us the vector perpendicular to both the vectors.

a vector * b vector = |a|.|b|.sin(X)

X is the angle between a vector and b vector.

In the same way, dot product of two vectors,

a vector . b vector = |a|.|b|.cos(X)

(a vector * b vector)^2 + (a vector . b vector)^2

= (|a|^2)(|b|^2)

{ As sin^(X) + cos(X)^2 = 1 }