Question

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

Answer 1

To find the values of a + b, 9a + 7b, |a|, and |a − b|, substitute the given values of a and b into the respective equations. The calculations give us: a + b = 16i − 8j − 2k, 9a + 7b = 117i − 105j + 84k, |a| = √194, and |a − b| = 18.

Step-by-step explanation:

To find the values of a + b, 9a + 7b, |a|, and |a − b|, we need to substitute the given values of a and b into the respective equations.

So, a = 9i − 8j + 7k and b = 7i − 9k.

Substituting the values, we get:

a + b = (9i − 8j + 7k) + (7i − 9k) = 16i − 8j − 2k.

9a + 7b = 9(9i − 8j + 7k) + 7(7i − 9k) = 117i − 105j + 84k.

|a| = √((9)² + (-8)² + (7)²) = √(81 + 64 + 49) = √194.

|a − b| = √((9 − 7)² + (-8 − 0)² + (7 − (- 9))²) = √(2² + (-8)² + 16²) = √(4 + 64 + 256) = √324 = 18.

Answer 2

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

4) |a-b|

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