find a vector of length 3 which has A.)the smae direction as 5i-2j
B.)the opposite direction to 4i+5j
To be "in the same direction" means that the vector you're looking for has the same ratio of components i and j as the original vector. You're starting with the vector $\displaystyle 5 \vec i - 2 \vec j$, whose magnitude is $\displaystyle \sqrt {29}$. So to have a vector of magintude 3 in the same direction simply multiply $\displaystyle 5 \vec i - 2 \vec j $ through by $\displaystyle 3/\sqrt {29} $.
To be in the opposite direction of a given vector, simply reverse the signs or the $\displaystyle \vec i $ and $\displaystyle \vec j $ components. So the opposite of vector $\displaystyle 4 \vec i + 5 \vec j $ is: $\displaystyle -4 \vec i - 5 \vec j $. Then apply the same length correction as above.