Question

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

Answer 1

(c)

"The given statement is true, by definition of length of a vector
`v`,
`||v|| = √(v\bullet v)`"

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|| = √(v\bullet v)`"