Let `vec(u)=hat(i)-hat(j), vec(v)=2hat(i)+5hat(j), vec(w)= 4 hat(i)+3hat(j) and vec(p) = vec(u) + vec(v)+vec(w)`. Which one of the following is correct ?

Options

A. `-3vec(u)+2vec(v)=vec(p)`
B. `3vec(u)-2vec(v)=vec(p)`
C. `3vec(u)+2vec(v)=vec(p)`
D. `-3vec(u)-2vec(v)=vec(p)`

Answer

C

Explanation

Since, `vec(p) = vec(u)+vec(v)+vec(w)`
`rArr vec(p)=(hat(i)-hat(j))+(2hat(i)+5hat(j))+(4hat(i)+3hat(j))=7hat(i)+7hat(j)`
Now, `3vec(u)+2vec(v)=3(hat(i)-hat(j))+2(2hat(i)+5 hat(j))=`
`3hat(i)-3hat(j)+4hat(i)+ 10 hat(j)=7hat(i) + 7hat(j)`
`rArr 3 vec(u)+2 vec(v)= vec(p)`