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# P3 May 2002 Q8d watch

1. Help for part d please:

I'll type out the whole question.

Referred to a fixed origin O, the points A, B and C have position vectors (9i - 2j + k), (6i + 2j + 6k) and (3i + pj + qk) respectively, where p and q are constants

a) Find, in vector form, an equation of the line l which passes through A and B.

Given that C lies on l

b) find the value of p and the value of q.
c) calculate in degrees, the acute angle between OC and AB.

The point D lies on AB and ii such that OD is perpendicular to AB.

OK - I can do parts a to c fine. But part d - in the markscheme it says you've got to obtain an equation in t (having used the scalar product), and solve it to obtain t = 0.6. They then use t to obtain 7.2i + 0.4j + 4k.

Can someone please tell me how they obtain this equation?
2. (Original post by foowise)
Help for part d please:

I'll type out the whole question.

Referred to a fixed origin O, the points A, B and C have position vectors (9i - 2j + k), (6i + 2j + 6k) and (3i + pj + qk) respectively, where p and q are constants

a) Find, in vector form, an equation of the line l which passes through A and B.

Given that C lies on l

b) find the value of p and the value of q.
c) calculate in degrees, the acute angle between OC and AB.

The point D lies on AB and ii such that OD is perpendicular to AB.

OK - I can do parts a to c fine. But part d - in the markscheme it says you've got to obtain an equation in t (having used the scalar product), and solve it to obtain t = 0.6. They then use t to obtain 7.2i + 0.4j + 4k.

Can someone please tell me how they obtain this equation?
fermat did this here: http://www.uk-learning.net/showthrea...448#post786448
3. (Original post by foowise)
Help for part d please:

I'll type out the whole question.

Referred to a fixed origin O, the points A, B and C have position vectors (9i - 2j + k), (6i + 2j + 6k) and (3i + pj + qk) respectively, where p and q are constants

a) Find, in vector form, an equation of the line l which passes through A and B.

Given that C lies on l

b) find the value of p and the value of q.
c) calculate in degrees, the acute angle between OC and AB.

The point D lies on AB and ii such that OD is perpendicular to AB.

OK - I can do parts a to c fine. But part d - in the markscheme it says you've got to obtain an equation in t (having used the scalar product), and solve it to obtain t = 0.6. They then use t to obtain 7.2i + 0.4j + 4k.

Can someone please tell me how they obtain this equation?

Ive done this question before .

What you do is find the Directional vectors of OD and AB.
Once youve got both of these, put them next to each other and compare.

You will notice that one of the Directional vectors will be x2 the other one, so the ratio is 2:1. Hope that helped.
4. Cheers - much appreciated.

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