Let x and y be vectors in R n . Prove that | | | x | | − | | y | | | ≤ | | x − y | | . [ Hint: For one part consider | | x + ( y − x ) | | and Exercise 25 .]
Let x and y be vectors in R n . Prove that | | | x | | − | | y | | | ≤ | | x − y | | . [ Hint: For one part consider | | x + ( y − x ) | | and Exercise 25 .]
Solution Summary: The author explains the Cauchy-Schwarz inequality and the Triangular inequality.
Let
x
and
y
be vectors in
R
n
. Prove that
|
|
|
x
|
|
−
|
|
y
|
|
|
≤
|
|
x
−
y
|
|
. [Hint: For one part consider
|
|
x
+
(
y
−
x
)
|
|
and Exercise
25
.]
Quantities that have magnitude and direction but not position. Some examples of vectors are velocity, displacement, acceleration, and force. They are sometimes called Euclidean or spatial vectors.
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