Finding Perpendicular Line & Area with Vector Method

[Kenji Liew]

1) If given a surface with the equation z=x^2+ y^2 and we need to find the parametric equation of line perpendicular to the tangent plane at the point (a, b, a^2+b^2).
We can find the del (x,y,z) and then substitute the point to the del and finally we write it into the parametric form of line(a+t(b)) ?

2) If ABCD is a square, M and N be the midpoint of AB and BC respectively. Lines AN and DM intersect at P, lines AN and CM intersect at Q, lines CM and DN intersect at R.
how we are going to show that the [area AMP+ area BMQN + area of CNR ]=area DPQR if we using vector method? Using the properties of addition and subtraction of vector?

 

[NoMoreExams]

This might be helpful to review for the first question: http://www.libraryofmath.com/tangent-planes-and-normal-lines.html

 

[Kenji Liew]

Thanks for your helpful tip for the first question .

 

[Chrisas]

I could be off base here, but try thinking about this. Have you learned about how to take the product of vectors? How many ways to do it are there? Have you been taught that one of them gives an area of a certain geometric shape? You might be able to use this fact to show the areas are equal.