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.

Step-by-step 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

$\sqrt{5^2+(-12)^2}\\\\=\sqrt{25+144}\\\\=\sqrt{169}\\\\=13$

4) |a-b| is given by

$\sqrt{(5+3)^2+(-12+6)^2}\\\\=\sqrt{8^2+6^2}\\\\=\sqrt{64+36}\\\\=\sqrt{100}\\\\=10$

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