# Show that CP is independent of the values of r and q and evaluate it (vectors)

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Question (part c): http://prntscr.com/s68muw

vector AC = 8i -4, vector BP = (r - 6)i + (q + 3)j and vector CP = (r - 8)i + (q + 4)j

How do I show CP is independent of p and r? If that was possible then r and q wouldn't be in the CP vector unless they were both equal to 0 (which they're not). And how do I 'evaluate' a vector?? I'm so confused...

vector AC = 8i -4, vector BP = (r - 6)i + (q + 3)j and vector CP = (r - 8)i + (q + 4)j

How do I show CP is independent of p and r? If that was possible then r and q wouldn't be in the CP vector unless they were both equal to 0 (which they're not). And how do I 'evaluate' a vector?? I'm so confused...

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#2

(Original post by

Question (part c): http://prntscr.com/s68muw

vector AC = 8i -4, vector BP = (r - 6)i + (q + 3)j and vector CP = (r - 8)i + (q + 4)j

How do I show CP is independent of p and r? If that was possible then r and q wouldn't be in the CP vector unless they were both equal to 0 (which they're not). And how do I 'evaluate' a vector?? I'm so confused...

**TSR360**)Question (part c): http://prntscr.com/s68muw

vector AC = 8i -4, vector BP = (r - 6)i + (q + 3)j and vector CP = (r - 8)i + (q + 4)j

How do I show CP is independent of p and r? If that was possible then r and q wouldn't be in the CP vector unless they were both equal to 0 (which they're not). And how do I 'evaluate' a vector?? I'm so confused...

Note that AP and BP do not have arrows over them, just like CP in (c). This means we are talking about the magnitude of the vectors, not the vectors themselves.

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(Original post by

You haven't yet used the information that AP = 2BP.

Note that AP and BP do not have arrows over them, just like CP in (c). This means we are talking about the magnitude of the vectors, not the vectors themselves.

**Pangol**)You haven't yet used the information that AP = 2BP.

Note that AP and BP do not have arrows over them, just like CP in (c). This means we are talking about the magnitude of the vectors, not the vectors themselves.

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(Original post by

I still don’t see how that helps...

**TSR360**)I still don’t see how that helps...

Then work out an expression for CP, again in terms of r and q. The equation you worked on in the first step should suggest itself to you at this point.

It will be easiest if you do all this not in terms of the actual magnitudes of the vectors, but in terms of the squares of the magnitudes of the vectors (just to save you having to keep wrapping everything in huge square roots).

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(Original post by

Start by writing an equation, in terms of r and q, for what it means to have AP = 2BP. It will have lots of terms and you won't be able to simplify it much, but do it anyway and then put it to one side.

Then work out an expression for CP, again in terms of r and q. The equation you worked on in the first step should suggest itself to you at this point.

It will be easiest if you do all this not in terms of the actual magnitudes of the vectors, but in terms of the squares of the magnitudes of the vectors (just to save you having to keep wrapping everything in huge square roots).

**Pangol**)Start by writing an equation, in terms of r and q, for what it means to have AP = 2BP. It will have lots of terms and you won't be able to simplify it much, but do it anyway and then put it to one side.

Then work out an expression for CP, again in terms of r and q. The equation you worked on in the first step should suggest itself to you at this point.

It will be easiest if you do all this not in terms of the actual magnitudes of the vectors, but in terms of the squares of the magnitudes of the vectors (just to save you having to keep wrapping everything in huge square roots).

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(Original post by

I don't really follow that. What are the lower case vectors? Where have you used the fact that AP = 2BP? In fact, where have you worked out any magnitudes at all?

**Pangol**)I don't really follow that. What are the lower case vectors? Where have you used the fact that AP = 2BP? In fact, where have you worked out any magnitudes at all?

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(Original post by

I’ve re-written the displacement vectors so I can re-arrange things better. I turned AP = 2BP into |p - a| = 2|p - b| then substituted p - a in the CP vector with 2(p - b) so I can solve the vector simultaneously to find r and q and then re-write the final vector in terms of A, B and C

**TSR360**)I’ve re-written the displacement vectors so I can re-arrange things better. I turned AP = 2BP into |p - a| = 2|p - b| then substituted p - a in the CP vector with 2(p - b) so I can solve the vector simultaneously to find r and q and then re-write the final vector in terms of A, B and C

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