Question

let vector OP = 2i + 3j and vector OQ = -6i+4j. R is a point on vector PQ such that PR/RQ = k/1, where k>0. a/ express vector OR in terms of k, i and j. b/ express (vector OP)dot(vector OR) and (vector OQ)dot(vector OR) in terms of k. c/ Find the value of k such that OR bisects angle POQ.

Answer 1

\(OP\bullet OQ=0\)

Answer 2

thanks what i am having the most trouble with is part c

Answer 3

you could use the law of sines...

Answer 4

\[\frac{PR}{\sin 45}=\frac{OR}{\sin a}\text{ and }\frac{QR}{\sin 45}=\frac{OR}{\sin b}\]\[\Rightarrow \frac{PR}{QR}=\frac{\sin b}{\sin a}\text{ but }a=90-b\Rightarrow \frac{PR}{QR}=\tan b\]

\[\cos b = \frac{OQ\bullet QP}{|\!|OQ|\!||\!|QP|\!| }\]

Answer 5

never thought of using law of sines for this vector problem

Answer 6

oops.

\[\tan b = \frac{|\!|OP|\!|}{|\!|OQ|\!|}\]

Answer 7

so that's k, right?

Answer 8

yes its good

Answer 9

did you draw a pic when you tried this prob?

Answer 10

yes but i got stuck after doing part b

Answer 11

what class is this?

Answer 12

precalculus honors

Answer 13

doing vectors? well, good on you!

Answer 14

well some teachers skip vectors but my teacher insists

Answer 15

that's good. if you ever take physics or linear algebra, you'll be ahead of the game!

Answer 16

you understand the prob now? I think it's always good to draw pics and label stuff. it can help generate ideas. and don't discard your intuition until you work it through. i've tossed ideas that were valid because i thought they would work but I didn't follow through on them to see the light at the end.
i'm sure you know and have a good feel for this.

good luck!

Answer 17

thanks and good night

Answer 18

thanks for the great question!