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Ede4ka [16]
3 years ago
11

Find a unit vector that is orthogonal to both u and v. u = −8, −6, 4 v = 10, −18, −2

Mathematics
1 answer:
Delvig [45]3 years ago
5 0
A vector w orthogonal to u and v can be obtained by the cross product of u and v, namely u x v.  Subsequently, u x  v may be reduced to a unit vector.

u<-8,-6,4>
v<10,-18,-2>

w=u x v 
=
  i      j   k
 -8   -6  4
10 -18 -2
=<12+72, 40-16, 144+60>
=<84, 24, 204>
=12 < 7,2,17>

Check that w is orthogonal to u and v
w.u = 12<7,2,17><-8,-6,4> = 12(-56-12,68)=0
w.v = 12<7,2,17><10,-18,-2> = 12(70-36-34)=0
Therefore w is orthogonal to both u and v.

Unit vector of w
\frac{}{\sqrt{7^2+2^2+17^2}}=\frac{1}{3\sqrt{38}}
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The picture below is pretty much all you need to know to answer these questions. It is a short course on arithmetic and geometric sequences. (We have left out some simplifications that can be made to the formulas for Nth term, and we have not shown formulas for the sum of a sequence.)

1. Geometric sequence with first term 5, common ratio 2. It will have the formula
.. f(n) = 5*2^(n-1) . . . . . . I can't read your picture to tell whether that is B or D

2. Arithmetic sequence with first term 1 and common difference 3. It will have the formula
.. f(n) = 1 +3(n -1) . . . . . . matches A

3. Geometric sequence with first term 2 and common ratio 3/2 = 1.5. It will have the formula
.. f(n) = 2*1.5^(n -1) . . . . . matches C

4. Geometric sequence with first term 600 and common ratio 60/600 = 0.1. It will have the formula
.. f(n) = 600*0.1^(n-1)
This can be simplified using the rules of exponents to
.. f(n) = 600*(0.1^-1)*(0.1^n)
.. f(n) = 6000*0.1^n . . . . . . matches A

5. The sequence is 12, 11, 10, 9, .... It is an arithmetic sequence with first term 12 and common difference -1. It will have the formula
.. f(n) = 12 +(-1)*(n -1)
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6. This is an arithmetic sequence with first term 8 and common difference -0.5. It will have the formula
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7 0
3 years ago
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svlad2 [7]
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3 0
3 years ago
Pete's checking account showed a balance at the beginning of the month of $180. After 3 days the checking account showed a balan
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Answer:

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3 years ago
What is the measurement of this angle
mafiozo [28]

Answer:

28°

Step-by-step explanation:

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Stay safe and have a wonderful day! Peace!✌

6 0
3 years ago
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Solve 5r2 – 12 = 68. {±4} {±5} {±3} {±6}
sashaice [31]

Hey there!

Assuming you meant

5r^2 - 12 = 68

If so, follow these steps so it can be a little bit easier to solve

Firstly, we have to add by 12 on each of your sides

5r^2 -12 +12 \\ \\ 68 + 12

5r^2 = 5r^2 \\ \\ 68 + 12 = 80

We get: 5r^2 =80

Now, we have divide by 5 on each of your sides

\frac{5r^2}{5} = \frac{80}{5}

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We get: r^2 = 16

r = ± \sqrt{16}

Therefore , your answer is:r = ±4

Good luck on your assignment and enjoy your day!

~LoveYourselfFirst:)

3 0
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