1. ## Vectors

find a vector of length 3 which has A.)the smae direction as 5i-2j
B.)the opposite direction to 4i+5j

2. Originally Posted by rabih2011
find a vector of length 3 which has A.)the smae direction as 5i-2j
B.)the opposite direction to 4i+5j
If $v$ is a vector and $k$ is a real number the $\dfrac{|k|}{||v||}v$ is a vector in the direction of $v$ with length $|k|$

3. 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 $5 \vec i - 2 \vec j$, whose magnitude is $\sqrt {29}$. So to have a vector of magintude 3 in the same direction simply multiply $5 \vec i - 2 \vec j$ through by $3/\sqrt {29}$.

To be in the opposite direction of a given vector, simply reverse the signs or the $\vec i$ and $\vec j$ components. So the opposite of vector $4 \vec i + 5 \vec j$ is: $-4 \vec i - 5 \vec j$. Then apply the same length correction as above.