Vectors Geometry proofs

[Hello_World]

For question 3 b) how do I find the value of k after I found OH
and I have the same problem for 3d) as well, I don't know what to do to find m and n

help appreciated thanks

 

[Deleted member 4993]

View attachment 33418
For question 3 b) how do I find the value of k after I found OH
and I have the same problem for 3d) as well, I don't know what to do to find m and n

help appreciated thanks

What did you get for length of OD? (1a)

What did you get for length of OH? (1b)

Please share your work'

Did you finish the problem that you posted at:

Binomial Identities

I'm just confused about where to start proving. Can anyone. help pls

www.freemathhelp.com

 

[Dr.Peterson]

View attachment 33418
For question 3 b) how do I find the value of k after I found OH
and I have the same problem for 3d) as well, I don't know what to do to find m and n

help appreciated thanks

In order to help, we need to see what expression you got for [imath]\overrightarrow{OH}[/imath]. You can't find k unless you have the right expression.

I myself found [imath]\overrightarrow{OH}[/imath] in terms of [imath]\overrightarrow{a}[/imath], [imath]\overrightarrow{b}[/imath], [imath]m[/imath], and [imath]n[/imath], before realizing I had to express [imath]m[/imath] and [imath]n[/imath] in terms of [imath]k[/imath] in order to do what they wanted. There is probably a more direct way! Start with [imath]k[/imath], expressing various vectors in terms of only that, [imath]\overrightarrow{a}[/imath], and [imath]\overrightarrow{b}[/imath].

(Notice, by the way, that the problem is misleading in writing a and b as if they were numbers, like k, m, and n, rather than vectors. It's important to make that distinction, as I have.)

 

[topsquark]

View attachment 33418
For question 3 b) how do I find the value of k after I found OH
and I have the same problem for 3d) as well, I don't know what to do to find m and n

help appreciated thanks

The marks you made on your diagram seem to indicate that you are taking AH = 1 and HD = k. This is not necessarily true. It could be that OH = 2 and HC = 2k. If you hadn't been given any lengths in the problem you would be okay to do this but you are given that OA = 2 and OB = 3. So the length scale is already set.

-Dan

 

[Dr.Peterson]

The marks you made on your diagram seem to indicate that you are taking AH = 1 and HD = k. This is not necessarily true. It could be that OH = 2 and HC = 2k. If you hadn't been given any lengths in the problem you would be okay to do this but you are given that OA = 2 and OB = 3. So the length scale is already set.

-Dan

I'm assuming those marks weren't meant to show actual lengths, but just reminders of the ratios. But I agree they are misleading, just as it is to write a as if it were a length.

For question 3 b) how do I find the value of k after I found OH
and I have the same problem for 3d) as well, I don't know what to do to find m and n

I finally sat down and worked out a solution to part b. The formula for [imath]\overrightarrow{OH}[/imath] is based on looking only at triangle AHD in terms of vectors, and not using m or n at all. Then we can find k by using the fact that [imath]\overrightarrow{OH}\perp\overrightarrow{AB}[/imath]. Assuming you know about the dot (scalar) product, you are essentially told what [imath]\overrightarrow{a}\cdot\overrightarrow{b}[/imath] is, and you can work out [imath]\overrightarrow{OH}\cdot\overrightarrow{AB}[/imath]. The problem could definitely have been written to say more clearly what you are expected to do, considering how many things one can try.

But we're still waiting for information about what you know and what you have done so far.