Vector Ratios: Solving for Unknowns | Homework Help

[abdo799]

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)

 

[Mark44]

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)

Show us how you arrived at these values.

 

[abdo799]

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?

 

[Mark44]

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?

There's no such thing as the ratio between two vectors, but you can calculate the ratio of their magnitudes or lengths.
The ratio OA:OB means |OA|/|OB|.

 

[abdo799]

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]

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

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
$$ \frac{|\vec{AP}|}{|\vec{PB}|} = \frac{|\vec{OA}|}{|\vec{OB}|}$$

 

[abdo799]

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
$$ \frac{|\vec{AP}|}{|\vec{PB}|} = \frac{|\vec{OA}|}{|\vec{OB}|}$$

okay..thanks