- #1
abdo799 said:Homework Statement
question attached
Homework Equations
The Attempt at a Solution
i can't understand III
i can't understand what he wants , if he wants the ratio , the ratio between AP and PB was 3/5
which is not the same as OA and OB
(λ=3/8)
There's no such thing as the ratio between two vectors, but you can calculate the ratio of their magnitudes or lengths.abdo799 said:Sure, the 3/8 ( i am sure it's correct ) was ii and it's a bit long to write it on the computer, but if it's important for you to know i can write it, as for iii.
As for AP, was mentioned that AP=λAB , AB=OB-OA=(2i+2j-2k)
AP= 3/8 * (2i+2j-2k) = ( 3/4 i + 3/4 j -3/4 k )
PB = OB-OP= (3i+4j) - (7/4 i + 11/4 j - 5/4 k )= (5/4 i+ 5/4 j - 5/4 k )
so ratio between them (if that's what he wants) is (5/4) / (3/4) =5/3
there is no ratio between OA and OB , what does he mean by (:) anyway?
You have a mistake in what you have for |AP| or |PB|.abdo799 said:i tried to come with the ratio between the magnitudes , they were not equal , AP:PB gave 15/16 and OA:OB gave 3/5
Mark44 said:You have a mistake in what you have for |AP| or |PB|.
When λ = 3/8,
AP = (3/4)<1, 1, -1>
and PB = (2 - 3/4)<1, 1, -1> = (5/4)<1, 1, -1>.
It makes it much simpler to simplify the vectors as I have done, before you calculate the magnitudes.
If you fix your mistake, you should be able to confirm that
$$ \frac{|\vec{AP}|}{|\vec{PB}|} = \frac{|\vec{OA}|}{|\vec{OB}|}$$
A vector is a mathematical object that has both magnitude (size) and direction. It is represented by an arrow, with the length of the arrow representing the magnitude and the direction of the arrow representing the direction.
A scalar is a mathematical object that has only magnitude (size) and no direction. It is represented by a single number. A vector, on the other hand, has both magnitude and direction.
The ratio between two vectors can be calculated by dividing the magnitude of one vector by the magnitude of the other vector. For example, if vector A has a magnitude of 5 and vector B has a magnitude of 10, the ratio between them would be 5/10 or 0.5.
No, vectors with different dimensions cannot be compared because they represent quantities in different directions and cannot be directly compared. However, they can be converted into a common dimension by using techniques such as vector projection.
Ratios between vectors can help us understand the relationship between different quantities and their directions. They can also be used to calculate important physical quantities such as velocity, acceleration, and force in physics and engineering applications.