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anonymous
 5 years ago
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.
anonymous
 5 years ago
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.

This Question is Closed

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Which parts are confusing to you?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Did you attempt anything so far?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0i 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

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0does that mean i have done a) and then im stuck on b?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0a is not quite right.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0wait, is the q vector 2i 4j + 3k ?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Oh, then yes that's right

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0So 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
 5 years ago
Best ResponseYou've already chosen the best response.0That should give you another nice system you can solve.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0haha ok, i might be back to confirm in a few minutes (maybe 10) :)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0does 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
 5 years ago
Best ResponseYou've already chosen the best response.0No, b has nothing to do with a.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0just plug in the given value for x and solve \[p \cdot q = 0\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0oh no, so i'm meant to do this?: 7i+5j +yk . q... cos 90 = 0

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0The dot product of two vectors: \[<a,b,c> \cdot <e,f,g>\ = ae + bf + cg\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0In your case you have x=7 so: p = <7,5,y> q = <2,4,3> \(\implies p \cdot q = 14  20 + 3y = 0\)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0oh, turns out i didn't know how to use dot product nor do i understand it.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0What class is this for?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0This is something you probably would have covered in a linear algebra class or some other introduction to vectors

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0The dot product of two vectors is the sum of the product of their components.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0gah sorry, i have no memory of doing vectors in high school, and this is 8 years later now

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0so y should be 11.3 recurring?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0np. 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
 5 years ago
Best ResponseYou've already chosen the best response.0If 14−20+3y=0 then 3y = 6 so y = 2

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0oh right, but you made x=7 into x=7 there :)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Well your original post said x = 7.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0I can't help it if I solve the problem you give me ;p

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0so it does, but thats not what the actual question says on the pdf i copied :) damn

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Ok well then it'd be 14  20 + 3y = 0 so 3y = 34 so y = 34/3

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0so to finish the question i have ot take the cross product of q and latest version of p?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Yes. That will give you a vector that is orthogonal to each. You recall how to take the cross product?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0add 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
 5 years ago
Best ResponseYou've already chosen the best response.0the angle between them is 90 actually

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.00 would mean they were parallel.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0thats cool then, now ill only have 4 more questions like that to get through today

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0so just to make sure im not making more silly mistakes, is the new vector for b) 14i  20j + 34k ?
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