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
Answer:
[tex]a+b=15i-4j-6k[/tex]
[tex]9a+3b=99i-36j[/tex]
[tex]|a| = 9i+4j+3k[/tex]
[tex]|a-b| = 3i+4j+12k[/tex]
Step-by-step explanation:
Given:
[tex]\begin{cases}a = 9i-4j+3k\\b=6i-9k\end{cases}[/tex]
[tex]\begin{aligned}a+b & = (9i-4j+3k)+(6i-9k)\\& = 9i-4j+3k+6i-9k\\& = 9i+6i-4j+3k-9k\\& = 15i-4j-6k\\\end{aligned}[/tex]
[tex]\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}[/tex]
[tex]\begin{aligned}|a| & = |9i-4j+3k|\\& = 9i+4j+3k\end{aligned}[/tex]
[tex]\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}[/tex]
