I hope someone can help me with this, I have never posted here before.
Given vectors a=(3,5) and b=(2,3). Find 5a-b.
Thanks if you can help me.
Multiplying a vector by a scalar (such as 5a here) multiplies each component
of the vector by the scalar (so 5a=(5*3, 5*5)=(15, 25)). Adding or
subtracting two vectors gives a vector whoese components are the sum of
difference of the corresponding components of the two vectors.
So:
5a-b=5(3, 5) - (2, 3) = (15, 25) - (2, 3) = (15-2, 25-3) = (13, 22)
RonL
Hello, Gretchen,
there isn't any trick to calculate the angle - only a simple formula:
Let $\displaystyle \alpha$ be the angle between the vectors $\displaystyle \vec a$ and $\displaystyle \vec b$ then you get the angle by:
$\displaystyle \cos(\alpha)=\frac{\vec a \cdot \vec b}{|\vec a| \cdot |\vec b|}$
Use this formula with your vectors:
$\displaystyle \cos(\alpha)=\frac{(5,2) (-2 ,5)}{\sqrt{5^2+2^2} \cdot \sqrt{(-2)^2+5^2}}=\frac{0}{29}$. Thus $\displaystyle \alpha = 90^\circ$
By the way: This result shows: Two vectors are perpendicular if their dot-product equals zero.
EB
PS: Please do us a favour and start a new thread if you have a new problem to do. Otherwise you risk that nobody will notice that you ask for some help again.
The formula is,
$\displaystyle \bold{u}\cdot \bold{v} = ||\bold{u} ||\cdot ||\bold{v}|| \cos \theta $
Where,
$\displaystyle \bold{u}\cdot \bold{v}$---> Dot product.
$\displaystyle ||\bold{u}||\cdot ||\bold{v}||$---> Product of their norms.
And,
$\displaystyle \cos \theta$ is the angle between them.