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VCE Specialist 3/4 Question Thread!

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bw304:
hi all, im really stuck on this question from my holiday homework:

A yacht sails from A to B on a bearing of 075* for 5km then from B to C on a bearing of 315* for 10km. Find:

a) the exact distance between A and C
b) the exact distance that the yacht is from A when it is closest to A on the BC leg.

for part a) i got 5√3 km (i don't have access to solutions so not sure if this is correct)
and I'm really stuck on part b). like how do you find out which point of BC is closest to A??

any help/hints would be appreciated !!!

caffinatedloz:

--- Quote from: bw304 on December 20, 2021, 06:49:14 pm ---like how do you find out which point of BC is closest to A??

any help/hints would be appreciated !!!

--- End quote ---
To find the point that is closest you'll need to use the distance formula. Find the distance between A and a point (x,y) where (x,y) lies on the line BC. (Do this by using the information about BC in the question to write y in terms of x).

Once you have the distance between the points in terms of x, find the derivative. Then set the derivative equal to 0 and solve for x. This will give you maximum and minimum points. Test the x value(s) and find the minimum x value. Then plug it back into your formula for BC to find the point.

If you have any more questions or want me to have a go at the working if you're still stuck just let me know! ;D

bw304:

--- Quote from: caffinatedloz on December 20, 2021, 07:46:15 pm ---To find the point that is closest you'll need to use the distance formula. Find the distance between A and a point (x,y) where (x,y) lies on the line BC. (Do this by using the information about BC in the question to write y in terms of x).

Once you have the distance between the points in terms of x, find the derivative. Then set the derivative equal to 0 and solve for x. This will give you maximum and minimum points. Test the x value(s) and find the minimum x value. Then plug it back into your formula for BC to find the point.

If you have any more questions or want me to have a go at the working if you're still stuck just let me know! ;D

--- End quote ---

oh yes that makes sense! thanks so much

galaxysauce:
Hi! Could someone please answer this question for 3bii.. Thanks!  :)

fun_jirachi:
Given two complex numbers \(u\) and \(v\), the midpoint of the two is always represented by \(\frac{u+v}{2}\).

What can you then deduce about \(M\) in this question?

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