text: please help in solving the following:? 1a) show that the equations to the straight line through     (a,b,c)parallel to the x-axis are y=b,z=c. 1b)  if !a!^2 + !b!^2 = !a+b!^2,then what is the relation between a & b. 1c)  find a unit vector perpendicular to the vectors i+j and j+k a)  not sure how you 'show' this... it's kind of trivial.  anything parallel to the x-axis is of the form y = constant, z = constant - and here the constants have to be b and c to go through the point, as there's no x dependence.  b)  |a+b|^2 = |a|^2 + a.b + |b|^2 so for it to balance, a.b = 0; that is, a and b are orthogonal.  c)  let the vector be (x,y,z).  then:  (1,1,0).(x,y,z) = 0  => x + y = 0 (0,1,1).(x,y,z) = 0  => y + z = 0  so x = z = -y, and the vector is parallel to (1,-1,1).  normalising this to unit length gives:  (1 / sqrt(3)) (1, -1, 1).