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Mathematics-Online problems:

Interactive Problem 119: Statements on Vector Algebra, Multiple-Choice

A B C D E F G H I J K L M N O P Q R S T U V W X Y Z
Let $ \vec{a}, \vec{b}, \vec{c}$ be vectors in $ \mathbb{R}^3$ . Decide whether the following statements are true or false.
a)
$ \vec{a} \times \vec{b} = \vec{0}$ implies that at least one of the two vectors $ \vec{a}, \vec{b}$ is the zero vector.
b)
The following holds: $ (\vec{a}-\vec{b})\times (\vec{a}+\vec{b})=2(\vec{a}\times \vec{b})$ .
c)
Every orthonormal basis form a right-handed system.
d)
The following holds: $ \big\vert\vert\vec{a}-\vec{c}\vert-\vert\vec{b}-\vec{c}\vert\big\vert\leq \vert\vec{a}-\vec{b}\vert$ .
e)
If vector $ \vec{a}$ is a multiple of vector $ \vec{b}$ , then $ [\vec{a}, \vec{b}, \vec{c}]=0$ .

Solution:
a) true      false
b) true false
c) true false
d) true false
e) true false


   

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  automatically generated: 8/11/2017