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Alchen [17]
3 years ago
8

In parts ​(a) through ​(e)​ below, mark the given statement as True or False. Justify each answer. All vectors are in set of rea

l numbers R Superscript nℝn. a. vtimes•vequals=Bold left norm v right normvsquared2 Choose the correct answer below. A. The given statement is false. It is not possible for it to be true because vtimes•v simplifies to a ​vector, whereas Bold left norm v right normvsquared2 simplifies to a scalar. B. The given statement is true. By the definition of the length of a vector v​, Bold left norm v right normvequals=StartRoot Bold v times Bold v EndRootv•v. C. The given statement is false. By the definition of the length of a vector ​v, Bold left norm v right normvequals=vtimes•v. It follows that Bold left norm v right normvsquared2equals=​(vtimes•v​)squared2. D. The given statement is true. By the definition of the length of a vector ​v, Bold left norm v right normvequals=vtimes•v. It follows that Bold left norm v right normvsquared2equals=​(vtimes•v​)squared2.
Mathematics
1 answer:
Oxana [17]3 years ago
5 0

Answer:

(c)

"The given statement is true, by definition of length of a vector v, ||v|| = \sqrt{v\bullet v}"

Step-by-step explanation:

(a) v  \bullet v = || v ||^2

That is completely correct Remember that if  v = (x_1,x_2,x_3)\\ then

v \bullet v = x_1*x_1+x_2*x_2+x_3*x_3 = x_1^2+x_2^2+x_3^2 = ||v||^2

Therefore the correct answer would be (c).

"The given statement is true, by definition of length of a vector v, ||v|| = \sqrt{v\bullet v}"

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