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# P3 Vectors watch

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1. With respect to an origin O, the position vectors of the points L and M are 2i - 3j + 3k and 5i + j + ck respectively, where c is a constant. The point N is such that OLMN is a rectangle.

a) Find the value of c

b) Write down the position vector of N

c) Find, in the form r = p + tq, an equation of the line MN

Cant do any of it, can anyone give me hand?
2. help, please, bump, bla bla bla
3. OL and ON are perpendicular, so dot product is 0. Solve to find c

The line MN is
r = M + t(-OL)
4. (Original post by imasillynarb)
With respect to an origin O, the position vectors of the points L and M are 2i - 3j + 3k and 5i + j + ck respectively, where c is a constant. The point N is such that OLMN is a rectangle.

a) Find the value of c

b) Write down the position vector of N

c) Find, in the form r = p + tq, an equation of the line MN

Cant do any of it, can anyone give me hand?

5. (Original post by Silly Sally)
a) Find c:

LM = 3i + 4j + (c-3)k
OL = 2i - 3j + 3k

these are perpendicular.. therefore (2i - 3j + 3k)(3i + 4j + (c-3)k) = 0

6 - 12 + 3(c-3) = 0

c = 15/3 = 5

c = 5, correct?
6. (Original post by Sahir)
a) Find c:

LM = 3i + 4j + (c-3)k
OL = 2i - 3j + 3k

these are perpendicular.. therefore (2i - 3j + 3k)(3i + 4j + (c-3)k) = 0

6 - 12 + 3(c-3) = 0

c = 15/3 = 5

c = 5, correct?
Yes
7. (Original post by Sahir)
a) Find c:

LM = 3i + 4j + (c-3)k
OL = 2i - 3j + 3k

these are perpendicular.. therefore (2i - 3j + 3k)(3i + 4j + (c-3)k) = 0

6 - 12 + 3(c-3) = 0

c = 15/3 = 5

c = 5, correct?
Thanks - how do you do part b?
8. (Original post by imasillynarb)
Yes
Heh i'm glad, cuz i gave up with the rest! to be honest with you i've not seen any questions on P3 which are GCSE-style vectors questions like in ex.5A of that Heinemann text book, do you know what i mean?
9. Cant do b) help!!

N = xi + yk + zk

I did, ON is perpendicular to OL

Meaning 2x - 3y + 3z = 0

Now Im stuck..
10. (Original post by imasillynarb)
Cant do b) help!!

N = xi + yk + zk

I did, ON is perpendicular to OL

Meaning 2x - 3y + 3z = 0

Now Im stuck..
PLEASE give me the answers - sometimes i work back from ans
11. (Original post by Silly Sally)
PLEASE give me the answers - sometimes i work back from ans
5, 3i + 4j + 2k
12. ON = OM - OL = (3, 4, 2)
13. b) Write down the position vector of N

The position vector of N is ON, and this is equal to LM. This is just OM - OL.

so this gives (3, 4, 2)

c) Find, in the form r = p + tq, an equation of the line MN

this is just:

OM + t(OL)

as OM is a vector onto the line,

and OL is a vector parallel.

Hope this helps.
14. Yeh ive done it now, cheers everyone

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