Question

hey guys! new here, please help
Let OP = 2i + 3j and OQ = -6i + 4j. Let R be a point on PQ such that PR : RQ = k : 1,
where k > 0.
(a) Express OR in terms of k, i and j.

Answer 1

hehehe... rely on others take so much time. I try once.

Answer 2

Let OQ =\(\vec q\)
\(OP=\vec p\)
\(OR =\vec r\)

Answer 3

the proportion is \(\dfrac{PR}{RQ}=\dfrac{k}{1}\) that is PR = k RQ

Answer 4

and we have \(vec {QP}=\vec p-\vec q\)

Answer 5

\(\vec QR =(1/k)\vec PR\)

Answer 6

hence we can go from O to R by

Answer 7

that is \(\vec q +\vec {QR}\)

Answer 8

as above, \(\vec{QR}=\dfrac{\vec{QP}}{k}=\dfrac{\vec p-\vec q}{k}\)

Answer 9

Replace all, we have \(\vec {OR}= \vec q+\dfrac {\vec p-\vec q}{k}\)

Answer 10

All you need is replace \(\vec q= 2i+3j\) and \(\vec p= -6i+4j\)

Answer 11

ok, let me do it to save time. I need review also

Answer 12

\(\vec {OR}=(2i+3j) + \dfrac{(-6i+4j )-(2i+3j)}{k}=(2i+3j) + \dfrac{(-8i+j )}{k}\)

Answer 13

That is the answer

Answer 14

um i dont think so because the answer here doesnt match imsp206.netvigator.com/~norme/Main/Maths/AMA/Rev-old.pdf

Answer 15

[Solution]
(a) OR =
+1
+
k
OP kOQ
=
2 - 6k
k + 1 i +
3 + 4k
k + 1 j

Answer 16

hehehe.. if it is so, I am sorry for my dumb solution.