Answer:
a.[tex]3u=3u_1\hat{i}+3u_2\hat{j}[/tex]
b.3u+5v=[tex](3u_1+5v_1)\hat{i}+(3u_2+5v_2)\hat{j}[/tex]
c.v-5u=[tex](v_1-5u_1)\hat{i}+(v_2-5u_2)\hat{j}[/tex]
Step-by-step explanation:
Let given vector u and v are
[tex]u=<u_1,u_2>[/tex]
[tex]v=<v_1,v_2>[/tex]
a.We have to find 3u
We are multiplying u by 3 then we get
[tex]3u=<3u_1,3u_2>[/tex]
[tex]3u=3u_1\hat{i}+3u_2\hat{j}[/tex]
b.We have ton find the value of 3u+5v
We are multiplying u by 3
3u=<3u_1,3u_2>
We are multiplying v by 5 then we get
[tex]5v=<5v_1,5v_2>[/tex]
Adding 3u with 5v then we get
[tex]3u+5v=<3u_1+5v_1,3u_2+5v_2>[/tex]
[tex]3u+5v=(3u_1+5v_1)\hat{i}+(3u_2+5v_2)\hat{j}[/tex]
c.We have to find the value of v-5u
We are multiplying u by 5 then we get
[tex]5u=<5u_1,5u_2>[/tex]
Now,v-5u=[tex](v_1,v_2)-5(u_1,u_2)[/tex]
v-5u=[tex](v_1-5u_1)\hat{i}+(v_2-5u_2)\hat{j}[/tex]
