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mina [271]
3 years ago
12

Find a.b. a=3i+2j-k, b=4i+5k

Mathematics
1 answer:
Tomtit [17]3 years ago
5 0

Answer: a\cdot b= 7

Step-by-step explanation:

We are given

a=3\hat{i}+2\hat{j}-\hat{k}

b=4\hat{i}+5\hat{k}

They can be written as

a=3\hat{i}+2\hat{j}+(-1)\hat{k}

b=4\hat{i}+0.\hat{j}+5\hat{k}

Now , the dot product of and b is given by :-

\Rightarrow\ a\cdot b= (3\hat{i}+2\hat{j}+(-1)\hat{k})\cdot(4\hat{i}+0.\hat{j}+5\hat{k})

\Rightarrow\ a\cdot b=3\cdot 4 \cdot\hat{i}\cdot\hat{i}+2\cdot0\cdot\hat{j} \cdot\hat{j}+ (-1)\cdot 5 \cdot \hat{k}\cdot \hat{k}

\Rightarrow\ a\cdot b=12 \cdot\hat{i}^2+0-5 \cdot \hat{k}^2

\Rightarrow\ a\cdot b=12 \cdot(1)+0-5 \cdot (1)[Since \hat{i}^2=\hat{k}^2=1]

\Rightarrow\ a\cdot b=12 -5=7  

Therefore , the value of the dot product a\cdot b= 7

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Please solve the whole page please please
Leya [2.2K]

1d) ↑ (Do the same but turned if that's easier)

1a) 199

1b) 193

1c) 217

1e) Based on the box plot, we can for example, find the lowest and greatest values, the range (largest - smallest), the mean (all values / # values), and the median middle value or q2 given by the second line in the box.

2b) 7

2c) 9.5

2d) ↑

2e) because the data is not ordered, it is difficult to determine the quartile data. Once it is ordered like 6, 7, 7, 7, 8, 8, 9, 10, 10. The data can be visualized alot easier. With the box plot we can determine q3 of the data by looking at the 3rd line, using the whiskers of the box to find the minimum and maximum values.

3)

You need to find the minimum, maximum, the quartile data obtained by having an even amount of data on both sides, order it so that values can be grouped. this includes q1, q2 (or median), and q3.

In this case the ordered data would be: 4,6,8,8,9,11,12,14,14,16.

[4, 6, 8, 8, 9] [] [11, 12, 14, 14, 16]

4 is the minimum, 16 is the maximum, q1 is 8, q3 is 14, and median is 10.

4) ↑

5)

You need to find the minimum, maximum, the quartile data obtained by having an even amount of data on both sides, order it so that values can be grouped. this includes q1, q2 (or median), and q3.

In this case the ordered data would be:

45, 45, 50, 55, 60, 70, 70, 75, 80, 85

[45, 45, 50, 55, 60] [] [70, 70, 75, 80, 85]

45 is the minimum, 85 is the maximum, q1 is 50, q3 is 75, and median is 65.

6) ↑

4 0
2 years ago
Can you help me with this question?
Rufina [12.5K]

Answer:

  16.2

Step-by-step explanation:

The angle internal to the triangle at B is the supplement of the one shown, so is 65°. That is equal to the angle internal to the triangle at D. Since the vertical angles at C are congruent, the two triangles are similar by the AA theorem.

Corresponding sides of similar triangles are proportional, so we can write the proportion shown in the attachment:

  BC/FC = DC/AC

  BC = FC(DC/AC) = 21.6(7.2/9.6)

  BC = 16.2 . . . . matches the first choice

4 0
3 years ago
An item is regularly priced at $83. It is now priced at a discount of 55% off the regular price.
mart [117]

Answer:

$45.65 total

Step-by-step explanation:

6 0
3 years ago
Read 2 more answers
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maria [59]
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Answer:

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Scott divides some 4- digit numbers by 1000 and his answer is a decimal every time.  

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