Answer:
Evaluations take place in the following manner.
Step-by-step explanation:
We are given the following information in the question:
[tex]a = 9i-8j+7k\\b = 7i-9k[/tex]
We have to evaluate the following:
1) a+b
[tex]a + b=16i - 8j-2k[/tex]
2) 9a+7b
[tex]9a+7b = 9(9i-8j+7k)+7(7i-9k) \\=(81i-72j+63k)+(49i-63k)\\ = 130i-72j+126k[/tex]
3)|a|
[tex]|a| = \sqrt{x^2 + y^2 + z^2}\\\text{where} ~a = xi + yj + zk\\\\|a| = \sqrt{81+64+49} = \sqrt{194} = 13.9283[/tex]
4) |a-b|
[tex]a-b = (9i-8j+7k)-(7i-9k) = 2i-8j+16k\\\\|a-b| = \sqrt{2^2 + (-8)^2+(16)^2} = \sqrt{324} = 18[/tex]
