Answer to Question #335172 in Analytic Geometry for math

Question #335172

By considering the angles between the vectors, show that a + b and a – b are

perpendicular when (a) = (b)


1
Expert's answer
2022-05-03T03:36:31-0400

We remind that for any two vectors "f_1" and "f_2"we have: "\\cos\\,(\\alpha)=\\frac{(f_1,f_2)}{|f_1||f_2|}," where "\\alpha" is the angle between "f_1" and "f_2", "|.|" denotes a norm of a vector and "(.,.)" denotes a dot (scalar) product. Consider the scalar product: "(a+b,a-b)." Using the properties of the scalar product, we get: "(a+b,a-b)=(a,a-b)+(b,a-b)=(a,a)-(a,b)+(b,a)-(b,b)=|a|^2-|b|^2".

Thus, in case "a=b" we receive: "(a+b,a-b)=0". It means that "cos(\\beta)=0", where "\\beta" is the angle between "a+b" and "a-b". Thus, "\\beta=90^0" and it means that vectors are perpendicular.


Need a fast expert's response?

Submit order

and get a quick answer at the best price

for any assignment or question with DETAILED EXPLANATIONS!

Comments

No comments. Be the first!

Leave a comment

LATEST TUTORIALS
New on Blog
APPROVED BY CLIENTS