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horrorfan [7]
3 years ago
15

Picture shows question

Mathematics
1 answer:
GalinKa [24]3 years ago
5 0
All work is show in the picture below.

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Find a nonzero vector orthogonal to the plane through the points: ????=(0,0,1), ????=(−2,3,4), ????=(−2,2,0).
ser-zykov [4K]

Answer:

The nonzero vector orthogonal to the plane is <-9,-8,2>.

Step-by-step explanation:

Consider the given points are P=(0,0,1), Q=(−2,3,4), R=(−2,2,0).

\overrightarrow {PQ}==

\overrightarrow {PR}==

The nonzero vector orthogonal to the plane through the points P,Q, and R is

\overrightarrow n=\overrightarrow {PQ}\times \overrightarrow {PR}

\overrightarrow n=\det \begin{pmatrix}i&j&k\\ \:\:\:\:\:-2&3&3\\ \:\:\:\:\:-2&2&-1\end{pmatrix}

Expand along row 1.

\overrightarrow n=i\det \begin{pmatrix}3&3\\ 2&-1\end{pmatrix}-j\det \begin{pmatrix}-2&3\\ -2&-1\end{pmatrix}+k\det \begin{pmatrix}-2&3\\ -2&2\end{pmatrix}

\overrightarrow n=i(-9)-j(8)+k(2)

\overrightarrow n=-9i-8j+2k

\overrightarrow n=

Therefore, the nonzero vector orthogonal to the plane is <-9,-8,2>.

8 0
3 years ago
What value should go in the red box​
NeX [460]
I’m pretty sure it would be 4, since y= (x) which would be the numbers on the chart and then add 2
ex: y= (2) + 2
y= 4 and so on
6 0
3 years ago
Read 2 more answers
Is 144 a perfect square or not​
Rina8888 [55]

Answer: Yes

Step-by-step explanation: 144 is a perfect square. In other words, it's possible to find a whole number that can be multiplied by itself that gives us 144.

In this case, we multiply 12 by 12 or 12² to get 144 which means 144 is a perfect square. Also, it's on our perfect square list which I will attach below.

6 0
3 years ago
If i won 10 games out of 16, how many games would i need to paly to win 50
MrRa [10]
Ratio is 10:16, so to win 50, its 50:190, so you need to play 190 games to win 50
7 0
3 years ago
Read 2 more answers
Simplify the expression. Rewrite using only positive exponents.
ivanzaharov [21]

The simplification form of the provided expression is x¹⁸a³b³ option

(d) x¹⁸a³b³ is correct.

<h3>What is an integer exponent?</h3>

In mathematics, integer exponents are exponents that should be integers. It may be a positive or negative number. In this situation, the positive integer exponents determine the number of times the base number should be multiplied by itself.

It is given that:

The expression:

= \rm (\dfrac{x^4a^2b^3}{x^{-2}ab^2})^3

After using the integer exponent property:

\rm =\dfrac{x^{12}a^6b^9x^6}{a^3b^6}

= a³b³x¹⁸ Or

=x¹⁸a³b³

Thus, the simplification form of the provided expression is x¹⁸a³b³ option

(d) x¹⁸a³b³ is correct.

Learn more about the integer exponent here:

brainly.com/question/4533599

#SPJ1

4 0
2 years ago
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