Answer :
Answer: 1) [tex]2\hat{i}-18\hat{j}[/tex] 2) [tex]\hat{i}-6\hat{j}[/tex] 3) 13, 4) 10.
Step-by-step explanation:
Since we have given that
[tex]\vec{a}=5\hat{i}-12\hat{j}\\\\and\\\\\vec{b}=-3\hat{i}-6\hat{j}[/tex]
So, we need to find :
1) a + b is given by
[tex]5\hat{i}-12\hat{j}-3\hat{i}-6\hat{j}\\\\=2\hat{i}-18\hat{j}[/tex]
2) 2a+3b is given by
[tex]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}[/tex]
3) |a| is given by
[tex]\sqrt{5^2+(-12)^2}\\\\=\sqrt{25+144}\\\\=\sqrt{169}\\\\=13[/tex]
4) |a-b| is given by
[tex]\sqrt{(5+3)^2+(-12+6)^2}\\\\=\sqrt{8^2+6^2}\\\\=\sqrt{64+36}\\\\=\sqrt{100}\\\\=10[/tex]
Hence, 1) [tex]2\hat{i}-18\hat{j}[/tex] 2) [tex]\hat{i}-6\hat{j}[/tex] 3) 13, 4) 10.