If `vec(a) = hat(i) + 2 hat(j) + 3 hat(k)` and `vec(b) = 2 hat(i) + 3 hat(j) + hat(k)` , find a unit vector in the direction of `( 2 vec(a) + vec(b))`.

If vec(a) = hat(i) + hat(j) + 2 hat(k) and vec(b) = 3 hat(i) + 2 hat(j) - hat(k) , find the value of (vec(a) + 3 vec(b)) . ( 2 vec(a) - vec(b)) .

If vec(a)=hat(i)+hat(j)-4hat(k) " and " vec(b)=4hat(i)-hat(j)-2hat(k) , then find (i) a unit vector in the direction of the vector (2vec(a)-vec(b)) and (ii) vector and scalar components of the vector (2vec(a)-vec(b)) along coordinate axes.

For given vectors vec a = 2 hat i - hat j + 2 hat k and vec b = - hat i + hat j - hat k , find the unit vector in the direction of the vector vec a + vec b .

If vec(a)=hat(i)+2hat(j)-hat(k) " and " vec(b)=3hat(i)+hat(j)-5hat(k) , find a unit vector in a direction parallel to vector (vec(a)-vec(b)) .

If vec(a)=2hat(i)-hat(j)+2hat(k) and vec(b)=6hat(i)+2hat(j)+3hat(k) , find a unit vector parallel to vec(a)+vec(b) .

If vec(a)=hat(i)+hat(j)+hat(k), vec(b)=2hat(i)-hat(j)+3hat(k) " and " vec(c)=hat(i)-2hat(j)+hat(k) find a unit vector in a direction parallel to vector (2vec(a)-vec(b)+3vec(c)) .

If vec(a)=4hat(i)-hat(j)+hat(k) and vec(b)=2hat(i)-2hat(j)+hat(k) , then find a unit vector parallel to the vector vec(a)+vec(b) .

For given vector, vec a = 2 hat i j +2 hat k and vec b = - hat i + hat j - hat k , find the unit vector in the direction of the vector vec a + vec b .