1. ## Please help w/ vector question: Given that MPN is straight line, find value of k

Hi, I'm not sure if this is the right category for this type of question, but here it is anyway
vector.jpg
I'm entirely stuck and have no idea how to continue.
I get that AB = b-a and MN = -0.5b + a + 2b but that's as far as I've got in terms of finding k.

2. ## vector help

Originally Posted by jamesmith11
Hi, I'm not sure if this is the right category for this type of question, but here it is anyway
vector.jpg
I'm entirely stuck and have no idea how to continue.
I get that AB = b-a and MN = -0.5b + a + 2b but that's as far as I've got in terms of finding k.

I too would like to see a solution for this problem

3. ## Solution

What we know:

1. MN is -1/2b + 3a
2. PN is -k(b-a) + 2a
3. MP is -1/2b + a + k(b-a)

How to find K:

1. PN is on the same line as MN
2. This means that the ratios of the coefficients of A and B must be the same
3. Some examples.jpg(example)
4. From understanding this, you work out the ratios of the coefficients of A and B from line MN
5. A:B is 3:-0.5 or in other words 6:-1 ratio
6. Then fully expand the vector of PN
7. -kb +ka + 2a = PN
8. the ratio of A to B is 2+K : -K
9. To find K you have to make the ratios equal and to do this you must put them in fractions

By Spambot

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