Question

Find a + b, 9a + 3b, |a|, and |a − b|. a = 9i − 4j + 3k, b = 6i − 9k

Answer 1

`a+b=15i-4j-6k`

`9a+3b=99i-36j`

`|a| = 9i+4j+3k`

`|a-b| = 3i+4j+12k`

Explanation:

Given:

`\begin{cases}a = 9i-4j+3k\\b=6i-9k\end{cases}`

`\begin{aligned}a+b & = (9i-4j+3k)+(6i-9k)\\& = 9i-4j+3k+6i-9k\\& = 9i+6i-4j+3k-9k\\& = 15i-4j-6k\\\end{aligned}`

`\begin{aligned}9a+3b & = 9(9i-4j+3k) + 3(6i-9k)\\& = 81i-36j+27k+ 18i-27k\\& = 81i+ 18i-36j+27k-27k\\& = 99i-36j\end{aligned}`

`\begin{aligned}|a| & = |9i-4j+3k|\\& = 9i+4j+3k\end{aligned}`

`\begin{aligned}|a-b| & = |(9i-4j+3k)-(6i-9k)|\\& = |9i-4j+3k-6i+9k|\\& = |9i-6i-4j+3k+9k|\\& = |3i-4j+12k|\\& = 3i+4j+12k\end{aligned}`

Answer 2

1) a + b = ?

→ (9i − 4j + 3k) + (6i − 9k)

→ 15i - 4j - 6k

2) 9a + 3b = ?

→ 9(9i − 4j + 3k) + 3(6i − 9k)

→ (81i - 36j + 27k) + (18i - 27k)

→ 99i - 36j

3) |a| = ?

→ |9i − 4j + 3k|

→ 9i + 4j + 3k

4) |a − b| = ?

→ |(9i − 4j + 3k) - (6i − 9k)|

→ |3i - 4j + 12k|

→ 3i + 4j + 12k