If `vec(A)=2hat(i)+hat(j)` and `vec(B)=hat(i)-hat(j)`, sketch vector graphically and find the component of `vec(A)` along `vec(B)` and perpendicular to `vec(B)`

Answer

Component of A along B;`1/2(hat(i)-hat(j)); Component of A perpendicular to B; 3/2(hat(i)+hat(j))`

Explanation

`vec(A)=2hat(i)+hat(j), vec(B)=hat(i)-hat(j)`
Component of A along B
`=(A*B)/B.hat(B)=Acos theta.hat(B)`
`(2-1)/sqrt(2).((hat(i)-hat(j)))/sqrt(2)=1/2(hat(i)-hat(j))`
Component of A perpendicular to B
`=vec(A)-("compon ent of" vec(A) "along" vec(B))`
`=2hat(i)+hat(j)-1/2(hat(i)-hat(j))=3/2hat(i)+3/2hat(j)=3/2(hat(i)+hat(j))`