Past exam of the mathematics course of the year 1 of the natural sciences course of the University of Cambridge / 2016 / Paper 2 / 11 / b

Table of contents
- Solution b

Solution

Take two edge vectors in the face,

b - a

and

c - a

. Their cross product is the face normal vector

n = (b - a) \times (c - a) = a \times b + b \times c + c \times a .

The face plane is

(r - a) \cdot n = 0

. Every term in

a \cdot n

except

a \cdot (b \times c)

vanishes, giving

r \cdot (a \times b + b \times c + c \times a) = a \cdot (b \times c) .

The scalar triple product is nonzero, so this normal cannot vanish.

 Ancestors (12)

 View article source

 Discussion (0)

There are no discussions about this article yet.

 Articles by others on the same topic (0)

There are currently no matching articles.

  See all articles in the same topic Create my own version