A Maths (2000 OLvl question) - Vectors

anpanman SG

The position vectors of the points P and Q relative to an origin Q are p and q respectively. The point R is such that vector OR = 3/4 vector OP and the point S is the mid-point of PQ.

Express vector OS in terms of p and q.

My steps are as follows:

vector PO + vector OQ gives you PQ = -p +q

vector OS = 0.5 (q-p)

Answer given is 0.5 (q+p). Well, not sure who is right, but surely you can't add the 2 vectors and divide them like what the answer did?

Thanks!

Mikethm SG

PQ = -p + q

PS = 0.5PQ

PS = 0.5( -p + q)

PO + OS = -0.5p + 0.5q

OS = OP - 0.5p + 0.5q

OS = p - 0.5p + 0.5q

OS = 0.5p + 0.5q

Typo adjusted

anpanman SG

PQ = -p + q

PS = 0.5PQ

PS = 0.5( -p + q)

PO + OS = -0.5p + 0.5q

OS = OP - 0.5p + 0.5q

OP = p - 0.5p + 0.5q

OP = 0.5p + 0.5q

Hi Mikethm!

You said that OS = OP - 0.5p + 0.5q

and

OP = 0.5p + 0.5q

So OS = (0.5 p + 0.5q) - 0.5p + 0.5q

= q

Why's the answer kinda weird?

TrueHeart SG

Hi Mikethm!

You said that OS = OP - 0.5p + 0.5q

and

OP = 0.5p + 0.5q

So OS = (0.5 p + 0.5q) - 0.5p + 0.5q

= q

Why's the answer kinda weird?

Hi anpanman,

Please let me slowly state down everything bit by bit.

OP=p and OQ=q, thus PQ = OQ - OP = q - p

Since S is in the middle of PQ, PS = 1/2 PQ = 1/2 ( q - p )

OS = OP + PS = p + [(1/2)q - (1/2)p] = (1/2)p + (1/2)q

I hope that I didn't make it too complicated for you.

Cheers

Mikethm SG

Hi Mikethm!

You said that OS = OP - 0.5p + 0.5q

and

OP = 0.5p + 0.5q

So OS = (0.5 p + 0.5q) - 0.5p + 0.5q

= q

Why's the answer kinda weird?

I didn't say OP = 0.5p + 0.5q

TrueHeart SG

I didn't say OP = 0.5p + 0.5q

Hi Mikethm,

I am sorry to say so, but you did write OP = 0.5p + 0.5q in the last line of your previous post, though it is probably a typo where you wanted to write OS instead.

Cheers.

Mikethm SG

Hi Mikethm,

I am sorry to say so, but you did write OP = 0.5p + 0.5q in the last line of your previous post, though it is probably a typo where you wanted to write OS instead.

Cheers.

oh ya... last 2 steps typo