@Mann Yep, to be honest I was always puzzled by vector calculus (based on the work of Green, Stokes, Kelvin...) because at my uni (Politecnico di Milano - Chemical Engineering) it's very common to find such language to describe transport phenomena (heat, mass and momentum transfer) ;)
$Let \vec A , \vec B , \vec C$ be three unit vectors , suppose that $\vec A . \vec B = \vec A .\vec C=0$ and the angle between $\vec B$ and $\vec C$ is $\pi /6$ then $\vec A = k (\vec B \times \vec C)$ and k is equal to.
@ParthKohli For what I can tell about two years at uni, professors are (a bit eccentric) humans, just be natural and show your passion and motives. Remember, they are not unhappy to see one person interested in their fields (whether conservative or not ;))
It's because every point on the image has to satisfy $x+y+z=0$, hence if $y$ and $x$ are fixed on the relation, then it's game over: just plug in the value of $z=-x-y$ and you've got the projected image of the parabola on the plane. Moreover, if you want the intersection, just solve $y^2=4ax$ and $y=1-x$
@Mann well I got 345 and didn't knew about the mysterious bonus extra 12 questions which could bring my score easily above 380 as I had only left 3 questions and then cs pilani, but hmm :(
