Question

Find a+b,2a+3b,IaI, and Ia-bI. a[5, -12], b=[-3, -6]

Answer 1

Answer: 1)
`2\hat{i}-18\hat{j}` 2)
`\hat{i}-6\hat{j}` 3) 13, 4) 10.

Explanation:

Since we have given that

`\vec{a}=5\hat{i}-12\hat{j}\\\\and\\\\\vec{b}=-3\hat{i}-6\hat{j}`

So, we need to find :

1) a + b is given by

`5\hat{i}-12\hat{j}-3\hat{i}-6\hat{j}\\\\=2\hat{i}-18\hat{j}`

2) 2a+3b is given by

`2(5\hat{i}-12\hat{j})+3(-3\hat{i}-6\hat{j})\\\\=10\hat{i}-24\hat{j}-9\hat{i}+18\hat{j}\\\\=\hat{i}-6\hat{j}`

3) |a| is given by

`√(5^2+(-12)^2)\\\\=√(25+144)\\\\=√(169)\\\\=13`

4) |a-b| is given by

`√((5+3)^2+(-12+6)^2)\\\\=√(8^2+6^2)\\\\=√(64+36)\\\\=√(100)\\\\=10`

Hence, 1)
`2\hat{i}-18\hat{j}` 2)
`\hat{i}-6\hat{j}` 3) 13, 4) 10.