Are Mu and Lambda the Key to Solving this Line Intersection Problem?

[lionely]

the lines l2[/SUB and l₃
are given by

l₁ : r = 10i + j + 9k + μ(3i+j+4k)

l₂: x= (y+9)/2= (z-13)/-3

l₃ r= -3i-5j-4k + λ(4i+3j+k)

where mu and lambda are parameters.

d) Show that AC=BC

A(4,-1,1) this was given, I calculated and got B as (5,-1,-2) and C (1,-2,-3)

This I what I did so far

I found AC ( -3,-1,-4)

BC(-4,-1,-1)

I also found the mods of AC and BC to see if they were equal but, they're not.

 

[SammyS]

the lines l2[/SUB and l₃
are given by

l₁ : r = 10i + j + 9k + μ(3i+j+4k)

l₂: x= (y+9)/2= (z-13)/-3

l₃ r= -3i-5j-4k + λ(4i+3j+k)

where μ and λ are parameters.

d) Show that AC=BC

A(4,-1,1) this was given, I calculated and got B as (5,-1,-2) and C (1,-2,-3)

This I what I did so far

I found AC ( -3,-1,-4)

BC(-4,-1,-1)

I also found the mods of AC and BC to see if they were equal but, they're not.

It looks like you haven't given us the whole problem, although we can read between the lines to figure out most of what's missing:

Two of the lines intersect at point A, which is at (4,-1,1).

Two of the lines intersect at point B.

Two of the lines intersect at point C.​

...

Now,

Calculate vector AC and see if its magnitude matches the magnitude of either of the other two vectors.

Added in Edit:

B is at (5,1,-2) not (5,-1,-2)

 

[lionely]

it doesn't Magnitude of AC is root 26

while magnitude of B is root 30 and C is root 14.

sorry!
I found BC and the magnitude of it is root 26! Thank you for pointing out the mistake in the coordinates of B!

 

[SammyS]

it doesn't Magnitude of AC is root 26

while magnitude of B is root 30 and C is root 14.

sorry!
I found BC and the magnitude of it is root 26! Thank you for pointing out the mistake in the coordinates of B!

Good deal !

 

[lionely]

Ummm there's is one more part to the question , It says write down the coordinates of the point D on AB such that CB is perpendicular to AB.

I'm not sure what to do... do I do something with the dot product?

 

[SammyS]

Ummm there's is one more part to the question , It says write down the coordinates of the point D on AB such that CB is perpendicular to AB.

I'm not sure what to do... do I do something with the dot product?

Well, using the dot product will be a good way to check your answer, but think about the overall situation.

Triangle ABC has

length AC = length BC .​

Where should point D be on AB so that ... looks like a typo ?

 

[lionely]

write down the coordinates of the point D on AB such that CD is perpendicular to AB.

 

[SammyS]

write down the coordinates of the point D on AB such that CD is perpendicular to AB.

OK! That makes sense.


Now,

Triangle ABC has

length AC = length BC .​

Where should point D be on AB so that CD is perpendicular to AB.

 

[lionely]

In the middle of AB?

 

[SammyS]

In the middle of AB?

Yes. D is the midpoint of AB .

 

[lionely]

LOL so wait I can find find AD then just get D and that's it?

 

[SammyS]

LOL so wait I can find find AD then just get D and that's it?

Yes. That's it.

You can check your result by seeing if the appropriate dot product is zero.

 

[lionely]

Thank you again for the help. Homework is now finished!