Vectors: E Maths

anpanman SG

A regular hexgon ABCDEF, has centre O. Vector OA = a , vector OB = b

I have given you guys the guiding questions. The actual question is below. Please explain to me how to prove in equilateral triangle. E Maths paper tomorrow, so yea, help is needed urgently.

Express as simply as possible , in terms of a and/or b,

Vector DO, AB, and DB

Explain why |a| = |b| = |b-a|

The points X,Y and Z are such that

Vector OX = a + b, Vector OY = a - 2b , and OZ = b - 2a

Express as simply as possible in terms of a and/or b,

Vector AX, Vector YX

Express as simply as possible in terms of a and/or b, the vector XZ

Show that triangle XYZ is equilateral. (This is the question)

wee_ws SG

Hi,

To show that XYZ is equilateral, we show that all three sides are equal in magnitude.

Vector XY = -3b, Vector YZ = -3a + 3b = 3(b - a), Vector XZ = -3a.

Now we consider their lengths, i.e. XY = 3|b|, YZ = 3|b - a|, XZ = 3|a|.

By the fact that |a| = |b| = |b - a| (because a regular hexagon is formed by six equilateral triangles), the lengths are equal and we are done.

Thanks and good luck!

Cheers,
Wen Shih