Question

what is the angle between (P+Q) and (P-Q)

Answer 1

let Angle between two vectors A and B = Ф
Then dot product = P Q Cos Ф = P . Q
magnitudes of vectors P and Q =  |P| and |Q| respectively.

angle between (P+Q) and (P-Q) vectors = 
  = Cos⁻¹  [(P+Q) . (P-Q)] / ( |P| |Q| )
  = Cos⁻¹  (|P|² - |Q|²)/(|P| |Q| )
  = Cos⁻¹ [ 1/|Q|  - 1/|P| ]

Answer 2

Answer:

let Angle between two vectors A and B = Ф

Then dot product = P Q Cos Ф = P . Q

magnitudes of vectors P and Q =  |P| and |Q| respectively.

angle between (P+Q) and (P-Q) vectors =  

 = Cos⁻¹  [(P+Q) . (P-Q)] / ( |P| |Q| )

 = Cos⁻¹  (|P|² - |Q|²)/(|P| |Q| )

 = Cos⁻¹ [ 1/|Q|  - 1/|P| ]

Explanation: