How would you determine whether the given vectors are orthogonal, parallel, or neither?

a. u= %26lt;-3,9,6%26gt;, v= %26lt;4,-12,-8%26gt;


b. u= i - j + 2k, v= 2i - j + k


c. u= %26lt;a, b, c%26gt;, v= %26lt;-b,a,0%26gt;

How would you determine whether the given vectors are orthogonal, parallel, or neither?
if there are two vectors A(x1,y1,z1) %26amp; B (x2,y2,z2)


|A| = sqrt( x1^2 + y1^2 + z1^2 )


then if x1/x2 = y1/y2 = z1/z2, then A is parallel to B


(short cut)


if A.B (dot product) ,





ie. x1 x2 + y1 y2 + z1 z2 = ___





equals 0 then vectors are orthogonal





equals (|A||B|), vectors are parallel





else they are neither and intersect...








a) vectors are parallel,





coz...... -3/4 = 9/-12 = 6/-8





b) u.v= 2 +1 +2 = 5 ..%26amp; (|u||v|)=6, so neither





c) u.v = -ab + ab + 0 = 0





so orthogonal