ajshfgsjkhgf vectors question

[BubbleWrapMan]

ABCD is a trapezium with AB parallel to DC. X and Y are midpoints of AD and BC respectively.

(It's laid out something like this)

  DC
 X  Y
A    B

a) Express (directed line segment) XY in terms of a and b where (directed line segment) AB = a and (directed line segment) DC = b
b) Show that XY is parallel to AB

[BubbleWrapMan]

I was thinking that, but the answer says (1/2)(a + b) which makes me think I'm missing something.

[cipherpol]

let and

or

[98.40_for_sure]

Ahhah totally forgot you could define new vectors

[BubbleWrapMan]

Ah nice. Thanks everyone. ^^

[98.40_for_sure]

Hey brightsky, why is a.b and a.a = 0?

[BubbleWrapMan]

I would have thought you'd just say something like

Since a and b are parallel, XY must be parallel to both, since a scalar multiplication of the sum of two parallel lines does not change the direction.

[98.40_for_sure]

AB = a
since a = kb, XY = 1/2(a+ka) = 1/2(k+1)a

thus parallel?

[BubbleWrapMan]

Yeah. You're allowed to put it in words though aren't you? I've done it in the past.

[98.40_for_sure]

Show that XY is parallel to AB.
Which means mathematical proof not 'explain'

[BubbleWrapMan]

Hmm. Good point.

[brightsky]

Hey brightsky, why is a.b and a.a = 0?

Woops, I was thinking cross product. Listen to 99.95_for_sure. :p