Question

|AxB|2+|A.B|2=|A|2 |B|2 ?

Answer 1

See below

Explanation:

`mathbf A times mathbf B = |mathbf A ||mathbf B| sin alpha \ hat (mathbf n)`

`mathbf A * mathbf B = |mathbf A ||mathbf B| cos alpha`

`implies |mathbf A times mathbf B|^2 + | mathbf A * mathbf B|^2 = |mathbf A |^2|mathbf B|^2 (color(red)(sin^2 alpha + cos^2 alpha))`