How do you determine if a vector is parallel, perpendicular, or neither?

Is there like a one step process where you can determine it?





Take this for example:


u=%26lt;8,5%26gt;


v=%26lt;-2,4%26gt;





Is this vector parallel, perpendicular, or neither? What are the process for each? How do u know when its not parallel, perpendicular, or neither?|||Hi,





If it's perpendicular, its dot product or scalar product will equal zero.





For vectors %26lt;x1, y1%26gt; and %26lt;x2, y2%26gt;, the dot product is x1*x2 + y1*y2. For your vectors, it is 8(-2) + 5(4) = -16 + 20 = 4. They are not perpendicular.





If they were parallel there would be a scalar you could multiply times the x and y of one vector to equal the other vector.





-2 times -4 equals 8 for the x values, but 4 times -4 does not equal 5. Therefore they are not parallel either.





By process of elimination, they are neither.





I hope that helps!! :-)|||u have to finde the slope of it if it is paralell it has to be equal ,for perpendicular the multiple of them has to be -1|||If two vectors are perpendicular to each other, then the dot product is zero:





ux*vx + uy*vy = 0





In your example: 8*(-2) + 5*4 = -16 + 20 = 4, so these vectors are not perpendicular to each other.








magnitude of u: um = sqrt( ux^2 + uy^2 )


magnitude of v: vm = sqrt( vx^2 + vy^2 )





If two vectors are parallel, then the dot product is equal to the product of the magnitudes:


ux*vx + uy*vy = um * uv





In your example,


um = sqrt( 64 + 25 ) = sqrt ( 89) = 9.434


uv = sqrt( 4 + 16 ) = sqrt( 20 ) = 4.472


The product = 42.190, but the dot product is 4, therefore these vectors are not parallel.





The angle between the vectors can be found like this:





cos(Th) = dot product / (product of magnitudes)





For this example: cos(Th) = 4 / 42.190 = 0.0948


Th = 1.476 radians = 84.560 degrees.|||Well you can take (8,5) and (2,4) and just put them on graph paper, we just started this unit in school too|||It's been decades since I did geometry, but I think the direction of u is atan(8/5); the direction of v is atan(-2/4). So the angle between them is 84.5 deg. Does my brain still work after all that time?|||For a pair of vectors with non-zero components, simply divide the components in a like manner. If the values are identical, then the vectors are parallel. If the values are equal in absolute value, but opposite in sign, then they're perpendicular. Failing those two tests, you get "neither."





If you end up having to divide by zero (which you won't do), then you have infinite slope, so only if both had a zero in the corresponding components would the vectors be parallel; if they have zeroes in the opposite components, then they're perpendicular. Failing those two tests, you get "neither."

Where can I get a cheap vector image of a peacock?

I am looking for a royalty free vector of a peacock. Preferably something that looks like an etching or woodblock print. I don't mind paying for it, but don't want to spend a fortune.|||Some good royalty free micro stock sites:





http://www.istockphoto.com/index.php





http://www.dreamstime.com/





http://www.123rf.com/|||Also try Shutterstock


http://www.shutterstock.com/cat.mhtml?la鈥?/a>

How do I convert a cartesian vector into spherical coordinates?

Specifically, how do I represent:





r(x,y,z) = xi + yj + zk





As a vector fuction of ro, theta and phi?|||ro^2 = x^2 + y^2 + x^2





ro = sqrt(x^2 + y^2 + x^2)





cos(phi) = z / ro





cos(theta) = x / (ro * sin phi)|||x=p*sin(phi)*cos(theta)


y=p*sin(phi)*sin(theta)


z=p*cos(phi)





So however you want to represent your r(x,y,z), just replace with these conversions.


r(x,y,z)=p*sin(phi)*[i*cos(theta)+j*si鈥?for example.

How do you invert a vector mask in Photoshop?

I created a vector mask, but it's masking out the wrong part.|||a simple way to do it would be to finish the mask in the shape you want, then convert it to a selection and choose the inverse selection.|||here try out what these guys are saying...been a while since Ive messed with vector masks





http://objectmix.com/adobe-photoshop/231鈥?/a>

In general, how would you sketch a vector that was n times a given vector? How would the lengths and headings?

In general, how would you sketch a vector that was n times a given vector? How are the lengths and headings of these two vectors related?|||The lengths would be n times as long as the original and the heading would be exactly the same.|||A scalar multiple of a vector is the same direction and 'scaled' in magnitude by the value.





That is, their 'headings' are the same, but their lengths are relative to the scalar by which they were multiplied.





Doug|||if n is a scalar and not a vector then the length of the vector changes by a factor of n (new length = old length * n) and the direction remains constant.





If n is another vector with magnitude n and a direction then the vectors are multiplied using vector multiplication rules and the resultant will have a different magnitude and direction.

Where I can get my logo converted to vector file with lowest price?

I run a small business and I have some logos to be converted to vector file,but my budget is very low.So


Where I can get my logo converted to vector file with lowest price? How much is it ?|||Email me with the specifics and a picture of your current logo. I understand your budget concerns and I'll work with you on the price.





mattymjb@yahoo.com|||I could convert these logos for you for cheap. I am a freelance graphic designer with over 10 years of experience. I work with many screen printers and other business owners on a daily basis converting their logos to vector format. I could probably do them each for $10. But I would have to see how complex they are first. Email me the logos and I will give you an exact price. I am ready to start on these ASAP.|||This company provide a eye-catching logo conversion service! Their price is very reasonable!


Look at this page to know more information！





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How to find a unit vector that is normal (perpendicular) to a plane determined by three points?

Find a unit vector that is normal (perpendicular) to the plane determined by the points A(1, - 1, 2)


,B(2,0, - 1) and C(0,2,1).





I have no idea whatsoever about how to solve this one. All help is really appreciated!|||Form two vectors with your points. e.g.





AB = (1, 1, -3) and AC = (-1, 3, -1).





The cross product of these will be normal to the plane. To get a unit normal, just divide the cross product by its magnitude.





v = AB x AC = (8, 4, 4).





||v|| = 鈭?8虏 + 4虏 + 4虏) = 4鈭?6).





n = v/||v|| = (2/鈭?6), 1/鈭?6), 1/鈭?6)).