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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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The fare without tip for the Metro Taxi is of 1 passenger and 9.5 miles is $27.83.

The given parameters:

  • <em>Number of passenger = 1</em>
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  • <em>Cost of first 0.2 mile = $0.75</em>
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The fare without tip for the Metro Taxi is calculated as follows;

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The total cost is calculated as follows;

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total cost = $27.83

Thus, the fare without tip for the Metro Taxi is of 1 passenger and 9.5 miles is $27.83.

The complete question is below:

Compute the fare without tip: 1 passenger, 9.5 miles. Round to nearest fifth of a mile when dividing.

Metro Taxi: first 1/5 mi= $0.75, each additional 1/5 mi= $0.55, each additional passenger= $1.50.

Learn more about cost per miles here: brainly.com/question/2513267

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