`vec(P)+vec(Q)` is a unit vector along x-axis. If `vec(P)= hat(i)-hat(j)+hat(k)`, then what is `vec(Q)`?

Find the projection of the vector vec(P) = 2hat(i) - 3hat(j) + 6 hat(k) on the vector vec(Q) = hat(i) + 2hat(j) + 2hat(k)

If vec(P)=hat(i)+hat(j)-hat(k) and vec(Q)=hat(i)-hat(j)+hat(k) , then unit vector along (vec(P)-vec(Q)) is :

If vec(P)=hat(i)+hat(j)-hat(k) and vec(Q)=hat(i)-hat(j)+hat(k) , then unit vector along (vec(P)-vec(Q)) is :

If vec a.hat i= vec a.( hat i+ hat j)= vec a.( hat i+ hat j+ hat k) , then find the unit vector vec a