Vector perpendiculars. explanation please!?!?

i still do not quite understand how to find the perpendicular of a vector.


for example given vector B =i hat 3 + j hat 4


find the vector perpendicular to vector B





also.....how do you find angles of vectors?


ex. given C= i hat 12 - j hat 5


find the angles vector C makes with the positive and negaitve axes?.

Vector perpendiculars. explanation please!?!?
Perpendicular vectors have a dot product of zero.





So if V=a*i+b*j and U=c*i+d*j are perpendicular, then





V dot U = 0


or


a*c + b*d = 0.





So if B=3*i+4*j, then to find a vector perpendicular to that,


A=x*i+y*j, we just set up the equation.


B dot A = 0


or


3x + 4y =0.





Notice that all we have to do is switch the components and make exactly one of them negative.





x=-4, y=3 works just fine.





There are an infinite number of possible answers, though, not just one. This is because saying it's perpendicular only specifies the line it's on. It doesn't say which way it points along that line or how long it is.





The angle is, as I posted earlier, given as follows:


if C=x*i+y*j, then


θ=arctan(y/x) if x%26gt;0.


θ=arctan(y/x)+pi if x%26lt;0.





If you're doing it in degrees, change pi to 180 degrees in the second question.





So if C=12i-5j, then


θ=arctan(-5/12) = -.3948 radians or -22.62 degrees.