Question: Let x, y, z R a) If ||x - z|| < 2 and ||y - z|| < 3, prove that ||x - y|| <
Let x, y, z ∈ Rʹʹ
a) If ||x - z|| < 2 and ||y - z|| < 3, prove that ||x - y|| < 5.
b) If ||x|| < 2, ||y|| < 3, and ||z|| < 4, prove that |x ∙ y - x ∙ z| < 14.
c) If ||x - y|| < 2 and ||z|| < 3, prove that |x ∙ (y - z) - y ∙ (x - z)| < 6.
d) If ||2x - y|| < 2 and ||y|| < 1, prove that | ||x - y||2 - x ∙ x| < 2.
e) If n = 3, ||x - y|| < 2, and ||z|| < 3, prove that ||x × z - y × z|| < 6.
f) If n = 3, ||x|| < 1, ||y|| < 2, and ||z|| < 3, prove that ||x ∙ (y × z)|| < 6.
Step by Step Solution
3.40 Rating (153 Votes )
There are 3 Steps involved in it
a x y x z z y 2 3 5 b By vector algebra and the CauchySchwarz inequality xyxz xyz ... View full answer
Get step-by-step solutions from verified subject matter experts
Document Format (1 attachment)
741-M-N-A-D-I (468).docx
120 KBs Word File