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1 year ago

Find A∩B,given A={0,2,4,6,8}and B={-2,-4}

Mathematics

1 answer:

frez [133]1 year ago

7 0

The set is empty since there are no common elements

<h3>Set theory</h3>

Given the following sets

A={0,2,4,6,8} and B={-2,-4}

Required sets

A n B

Since intersection means that we are to write out all the values common to the set A and B, hence the equivalent set will be;

A n B = {}

The set is empty since there are no common elements

Learn more on union of sets here: brainly.com/question/2166579

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Find the vector that has the same direction as 3, 2, −6 but has length 2.

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The vector is $\vec r = \left(\frac{6}{7},\frac{4}{7},-\frac{12}{7}\right)$ .

Step-by-step explanation:

We can determine the equivalent vector ( $\vec r$ ), dimensionless, by means of the following formula:

$\vec r = \frac{\vec u}{\|\vec u\|} \cdot \|\vec r\|$ (1)

Where:

$\vec u$ - Original vector, dimensionless.

$\|\vec u\|$ - Norm of the original vector, dimensionless.

$\|\vec r\|$ - Norm of the new vector, dimensionless.

The norm of the original vector is determined by the following definition:

$\|\vec u\| = \sqrt{\vec u\,\bullet \,\vec u}$ (2)

If we know that $\vec u = (3, 2, -6)$ , then the norm of the original vector is:

$\|\vec u\| = \sqrt{(3)\cdot (3)+(2)\cdot (2)+(-6)\cdot (-6)}$

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If we know that $\|\vec r\| = 2$ , then the new vector is:

$\vec r = \frac{2}{7}\cdot (3,2,-6)$

$\vec r = \left(\frac{6}{7},\frac{4}{7},-\frac{12}{7}\right)$

The vector is $\vec r = \left(\frac{6}{7},\frac{4}{7},-\frac{12}{7}\right)$ .

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