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!
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
Originally posted by Mikethm: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?
Originally posted by anpanman: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
Originally posted by anpanman: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
Originally posted by Mikethm: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.
Originally posted by TrueHeart: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