seeing:
A(4,0) B(2,1)
find a unit vector in the direction of AB ( smal arrow above AB that begins from left to right) abd a vector of magnitude 3 in the opposite direction
thank you
seeing:
A(4,0) B(2,1)
find a unit vector in the direction of AB ( smal arrow above AB that begins from left to right) abd a vector of magnitude 3 in the opposite direction
thank you
A unit vector is simply a vector with a magnitude of 1. To get the unit vector in the direction of the vector $\displaystyle \overrightarrow{A B}$, all you have to do is divide the components of the vector by its magnitude. This process is called normalization.
$\displaystyle \vec{AB}$
$\displaystyle = (2 - 4, 1 - 0)$
$\displaystyle = (-2, 1)$
Magnitude of $\displaystyle \vec{AB}$
$\displaystyle = \sqrt {{x}^{2}+{y}^{2}}$
$\displaystyle = \sqrt {{(-2)}^{2}+{1}^{2}}$
$\displaystyle = \sqrt {5}$
Unit vector in the direction of $\displaystyle \vec{AB}$
$\displaystyle = \left ( \frac{-2}{\sqrt{5}}, \frac{1}{\sqrt{5}} \right )$
To find the vector of magnitude 3 in the opposite direction of the vector $\displaystyle \vec{AB}$, you have to find the unit vector in the direction of $\displaystyle \vec{BA}$, which is in the opposite direction. Since the unit vector has a magnitude of 1, and you need a vector of magnitude 3, just multiply the unit vector by 3, and you'll get the answer.