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# C4 Vector and Integration

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1. I am struggling to understand the mark scheme of the following 2 questions. The mark schemes are really brief in its answers and don't really provide a full explanation. It would be greatly appreciated if someone could explain the steps to me.

For your reference both questions come from this practice paper: https://d3ee3dbb48c7712f2afa29150df9...%20Edexcel.pdf

This is the mark scheme: https://d3ee3dbb48c7712f2afa29150df9...%20Edexcel.pdf

Ok so the first question is vector - #4c

The second question is #8b
Attachment 538579538581
I have got to the second last step, so I am pretty sure I have got the integration part right. The problem might be the boundaries because I keep getting 10pie instead of 20pie. The boundaries I've got are 0 and pie.

Thanks anyone in advance for helping me out.
Attached Images

2. ok so
1. AB = OB - OA
cosx = a.b/|a||b|
(c) just basically asks you to write a vector formula for a line through a and b in odd wording, as the formula is technically just an equation for a general point on the line.
(d) perpendicular => dot product equal to zero. do dot product, solve equation for lambda.
(e) you have found where the two lines are perpendicular so just plug in your value for lambda into the equation for p.

y - y1 = m(x - x1)

your boundaries are fine but the problem is, from 0 to pi the curve only goes round the top half, so you've actually found the top half of the ellipse. all you have to do is multiply by two.
(if you go from 0 to 2pi you sum the top and bottom areas which = 0)
3. (Original post by Discipulus)
ok so
1. AB = OB - OA
cosx = a.b/|a||b|
(c) just basically asks you to write a vector formula for a line through a and b in odd wording, as the formula is technically just an equation for a general point on the line.
(d) perpendicular => dot product equal to zero. do dot product, solve equation for lambda.
(e) you have found where the two lines are perpendicular so just plug in your value for lambda into the equation for p.

y - y1 = m(x - x1)

your boundaries are fine but the problem is, from 0 to pi the curve only goes round the top half, so you've actually found the top half of the ellipse. all you have to do is multiply by two.
(if you go from 0 to 2pi you sum the top and bottom areas which = 0)

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