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# Vector Geometry!! watch

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1. this question is not tough,i think.
I just don't know how to solve it
WOuld u guys help me out

O is the origine.
OA=i + 2j
OB= -i+4j

1/2^0.5(i+j) is a unit vector perpenducular to AB

find the position vector of the foot of the perpendicular from the origin to the line segment AB.

2.

position vectors of A ,B,C,D and E are a , b,c,d,e respectively.
A is the midpt of OB and E divides AC in the ratio 1:2.
If e=1/3 d , show that OCDB is a parallelogram..

Thank you very much ...
2. (Original post by Fong_Leonard)
this question is not tough,i think.
I just don't know how to solve it
WOuld u guys help me out

O is the origine.
OA=i + 2j
OB= -i+4j

1/2^0.5(i+j) is a unit vector perpenducular to AB

find the position vector of the foot of the perpendicular from the origin to the line segment AB.

Thank you very much ...
find AB = OB - OA

The line going through the origin perp to AB is r = t/2^0.5(i+j) for a scalar t. Find the value of t for which the two lines cross
3. i don;t quite get it . why do u introduce the t .
and which equation do u compare to find out the value of t??
4. (Original post by Fong_Leonard)
i don;t quite get it . why do u introduce the t .
and which equation do u compare to find out the value of t??
The eqn of the line through AB is,
r1 = OA + λ(OB - OA)

The line passing thro' the origin parallel to the unit vetor v (let v=(1/√2)(i+j) ) is r2 = tv, say.
When r1 and r2 intersect, they are equal, so put r1=r2, and solve for λ and t.

I got (3/2)(i+j)
5. (Original post by Fong_Leonard)
.....

2.

position vectors of A ,B,C,D and E are a , b,c,d,e respectively.
A is the midpt of OB and E divides AC in the ratio 1:2.
If e=1/3 d , show that OCDB is a parallelogram..

Thank you very much ...
AC = c - a
OE = OA + (1/3)AC ( E divide AC in ratio 1:2)
OE = a + (1/3)(c - a)
OE = c/3 + 2a/3
==========

OD = 3OE, (e = d/3)
OD = c + 2a
CD = OD - OC
CD = c + 2a - c
CD = 2a
but,
OB = 2a (A is mid-pt of OB)
=> CD parallel to OB
=============

BD = OD - OB
BD = c + 2a - 2a
BD = c
but,
OC = c
=> BD parallel to OC
=============

=> OCBD is a parallelogram
==================
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