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sesenic [268]
4 years ago
9

Find a + b, 9a + 7b, |a|, and |a − b|. a = 9i − 8j + 7k, b = 7i − 9k

Mathematics
2 answers:
Evgesh-ka [11]4 years ago
7 0
A+b=9i-8j+7k+(7i-9k)
=9i-8j+7k+7i-9k
=16i-8j-2k
9a+7b=9(9i-8j+7k)+7(7i-9k)
=81i-72j+63k+49i-63k
=130i-72j
|a|=| 9i-8j+7k |
|a-b|=|9i-8j+7k-(7i-9k)|
=|9i-8j+7k-7i+9k|
=|2i-8j+16k|
i hope this is helping
Blababa [14]4 years ago
6 0

Answer:

Evaluations take place in the following manner.                    

Step-by-step explanation:

We are given the following information in the question:

a = 9i-8j+7k\\b = 7i-9k

We have to evaluate the following:

1) a+b

a + b=16i - 8j-2k

2) 9a+7b

9a+7b = 9(9i-8j+7k)+7(7i-9k) \\=(81i-72j+63k)+(49i-63k)\\ = 130i-72j+126k

3)|a|

|a| = \sqrt{x^2 + y^2 + z^2}\\\text{where} ~a = xi + yj + zk\\\\|a| = \sqrt{81+64+49} = \sqrt{194} = 13.9283

4) |a-b|

a-b = (9i-8j+7k)-(7i-9k) = 2i-8j+16k\\\\|a-b| = \sqrt{2^2 + (-8)^2+(16)^2} = \sqrt{324} = 18

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