anonymous
  • anonymous
this question is crushing my brain space!!! . Consider the vectors p = xi + 5j + yk and q = 2i 4j + 3k. a) For what values of x and y are the vectors p and q parallel? b) If x = 7 for what value of y are the vectors p and q perpendicular? Given that x and y takes these values nd a third vector that is perpendicular to both pand q.
Mathematics
  • Stacey Warren - Expert brainly.com
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schrodinger
  • schrodinger
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anonymous
  • anonymous
Which parts are confusing to you?
anonymous
  • anonymous
Did you attempt anything so far?
anonymous
  • anonymous
i did, and got something with a) if parallel then they are scalar multiples of each other... so ap=q then axi = 2j a5=-4 ay= 3 q=(2 -4 3) p= (x 5 y) a=-4/5 x = -0.4 y=-4/15

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anonymous
  • anonymous
does that mean i have done a) and then im stuck on b?
anonymous
  • anonymous
a is not quite right.
anonymous
  • anonymous
wait, is the q vector 2i -4j + 3k ?
anonymous
  • anonymous
yes
anonymous
  • anonymous
Oh, then yes that's right
anonymous
  • anonymous
So for b) you know that the dot product of two vectors is 0 if and only if they are perpendicular. So if they are perpendicular you know that the dot product of the two must be 0.
anonymous
  • anonymous
That should give you another nice system you can solve.
anonymous
  • anonymous
haha ok, i might be back to confirm in a few minutes (maybe 10) :)
anonymous
  • anonymous
does that mean i should be able to find j and k directions' magnitude when x=-7 by comparing the other values i got previously?
anonymous
  • anonymous
No, b has nothing to do with a.
anonymous
  • anonymous
just plug in the given value for x and solve \[p \cdot q = 0\]
anonymous
  • anonymous
oh no, so i'm meant to do this?: -7i+5j +yk . q... cos 90 = 0
anonymous
  • anonymous
no.
anonymous
  • anonymous
The dot product of two vectors: \[ \cdot \ = ae + bf + cg\]
anonymous
  • anonymous
In your case you have x=7 so: p = <7,5,y> q = <2,-4,3> \(\implies p \cdot q = 14 - 20 + 3y = 0\)
anonymous
  • anonymous
oh, turns out i didn't know how to use dot product nor do i understand it.
anonymous
  • anonymous
What class is this for?
anonymous
  • anonymous
http://www.maths.uq.edu.au/courses/MATH1050/
anonymous
  • anonymous
This is something you probably would have covered in a linear algebra class or some other introduction to vectors
anonymous
  • anonymous
The dot product of two vectors is the sum of the product of their components.
anonymous
  • anonymous
gah sorry, i have no memory of doing vectors in high school, and this is 8 years later now
anonymous
  • anonymous
so y should be 11.3 recurring?
anonymous
  • anonymous
np. Basically you just multiply each component pair, and add all those products. So if p = i + 2j + 3k and q = 4i + 3j - 2k Then \(p \cdot q = (1\cdot4) + (2\cdot 3) + (3 \cdot -2) = 4 + 6 -6 = 4\) The notable thing about the dot product is that if the two vectors are orthogonal (perpendicular) then the dot product will equal 0.
anonymous
  • anonymous
If 14−20+3y=0 then 3y = 6 so y = 2
anonymous
  • anonymous
oh right, but you made x=-7 into x=7 there :)
anonymous
  • anonymous
Well your original post said x = 7.
anonymous
  • anonymous
I can't help it if I solve the problem you give me ;p
anonymous
  • anonymous
so it does, but thats not what the actual question says on the pdf i copied :) damn
anonymous
  • anonymous
Ok well then it'd be -14 - 20 + 3y = 0 so 3y = 34 so y = 34/3
anonymous
  • anonymous
so to finish the question i have ot take the cross product of q and latest version of p?
anonymous
  • anonymous
Yes. That will give you a vector that is orthogonal to each. You recall how to take the cross product?
anonymous
  • anonymous
add the sum of the products of the components of the two vectors multiplied by the sine of the angle between them ... but that doesnt seem like it'll work cause sine 0 is 0 so i will end up with 0 which doesn't help
anonymous
  • anonymous
the angle between them is 90 actually
anonymous
  • anonymous
damn
anonymous
  • anonymous
0 would mean they were parallel.
anonymous
  • anonymous
thats cool then, now ill only have 4 more questions like that to get through today
anonymous
  • anonymous
=)
anonymous
  • anonymous
so just to make sure im not making more silly mistakes, is the new vector for b) -14i - 20j + 34k ?

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