Respuesta :
Answer: a) [tex]-1\hat{i}+1\hat{j}-2\hat{k}[/tex] b) [tex]2\hat{i}+\hat{j}+9\hat{k}[/tex] c) √14 d) √82.
Step-by-step explanation:
Since we have given that
[tex]\vec{a}=1\hat{i}+2\hat{j}-3\hat{k}\\\\\vec{b}=-2\hat{i}-\hat{j}+5\hat{k}[/tex]
So, we will first find :
1) a + b which is given by
[tex]\vec{a}+\vec{b}=1\hat{i}+2\hat{j}-3\hat{k}-2\hat{i}-\hat{j}+5\hat{k}\\\\\vec{a}+\vec{b}=-1\hat{i}+1\hat{j}-2\hat{k}[/tex]
2) 2a+3b is given by
[tex]2(1\hat{i}+2\hat{j}-3\hat{k})+3(-2\hat{i}-\hat{j}+5\hat{k})\\\\=4\hat{i}+4\hat{j}-6\hat{k}-6\hat{i}-3\hat{j}+15\hat{k}\\\\=-2\hat{i}+\hat{j}+9\hat{k}[/tex]
3) |a| is given by
[tex]|a|=\sqrt{1^2+2^2+(-3)^2}\\\\|a|=\sqrt{1+4+9}\\\\|a|=\sqrt{14}[/tex]
4) |a-b| is given by
[tex]|a-b|=\sqrt{(1+2)^2+(2+1)^2+(-3-5)^2}\\\\|a-b|=\sqrt{3^2+3^2+(-8)^2}\\\\|a-b|=\sqrt{9+9+64}\\\\|a-b|=\sqrt{82}[/tex]
Hence, a) [tex]-1\hat{i}+1\hat{j}-2\hat{k}[/tex] b) [tex]2\hat{i}+\hat{j}+9\hat{k}[/tex] c) √14 d) √82.
