[CIE] All Pure Mathematics (P1, P2 and P3) doubts here !

[Arthur Bon Zavi]

domain 0<=x<2pi

It's just pi not 2pi.

[astarmathsandphysics]

Transformation of curves
Multiple the graph of tanx by a factor 2 in the x direction and 3 in the y direction to get 3 tan(x/2)

[ashwinkandel]

One more question:

[astarmathsandphysics]

answered in attachment

[Arthur Bon Zavi]

@Arthur Bon Zavi If you can , can you plz show me show the graph looks like?? This is the first time i have come through a question in CIE Maths exam where graph of tanx has been asked to plot... I know how to plot for y=tanx ... but this y=3-tan(x/2)  for domain 0<=x<2pi seems complicated..

Have a look at the attachments. The red horizontal line on the positive axis is x = pi.

[ashwinkandel]

Thanks Arthur Bon Zavi .... Your help is really appreciated   

[Alpha]

Tuitions over, so I'll post my doubt here.

http://www.xtremepapers.com/CIE/International%20A%20And%20AS%20Level/9709%20-%20Mathematics/9709_s11_qp_31.pdf

No 3, on vectors.

Points A and B have coordinates (-1, 2, 5) and (2, -2, 11) respectively. The plane p passes through
B and is perpendicular to AB.

(i) Find an equation of p, giving your answer in the form ax + by + cz = d. [3]
(ii) Find the acute angle between p and the y-axis. [4]

How would you proceed with the second part?
I got the answer, but I checked the markscheme, and don't understand the procedures there.

[astarmathsandphysics]

The question is the same as finding the angle between (a,b,c) and (0,1,0)

[Alpha]

The question is the same as finding the angle between (a,b,c) and (0,1,0)

What will you take as (a,b,c)?
I took two points on the y-axis.

I cannot understand why Cambridge has taken vectors OB and OA. Shed some light please?

[Deadly_king]

What will you take as (a,b,c)?
I took two points on the y-axis.

I cannot understand why Cambridge has taken vectors OB and OA. Shed some light please?

I don't think I'll be of much help since I've forgotten most of my Maths by now

Anyway I'll try as much as I remember though am not so sure.....

To find the angle between a line and a plane we first have to find the angle between the normal of the plane and the direction vector of the line.

We need to find the direction vector of the normal of the plane by using OA and OB -----> OB - OA

Then you use the formula to find angle

[astarmathsandphysics]

Tabke abc as  (-1, 2, 5) - (2, -2, 11)=(-1-2,2--2,,5-1)=(-3,4,4)
a=-3
b=4
c=4

[Alpha]

I don't think I'll be of much help since I've forgotten most of my Maths by now

Anyway I'll try as much as I remember though am not so sure.....

To find the angle between a line and a plane we first have to find the angle between the normal of the plane and the direction vector of the line.

We need to find the direction vector of the normal of the plane by using OA and OB -----> OB - OA

Then you use the formula to find angle

Normal and direction vectors, sin formula, yes, I did.

But in the ER, OA is multiplied by OB. Gives you the answer, but I don't understand why.

No worries. Thank you though.

Tabke abc as  (-1, 2, 5) - (2, -2, 11)=(-1-2,2--2,,5-1)=(-3,4,4)
a=-3
b=4
c=4

(-1-2,2--2,,5-11)
c= -6.

I get what you mean. I did that too.

http://www.xtremepapers.com/CIE/International%20A%20And%20AS%20Level/9709%20-%20Mathematics/9709_s11_er.pdf

The examiners' report, on pg 22. It says by multiplying OA and OB. This is what I don't get.
Even YA's best contributors do not.

Appreciate your help. Thank you Sir.  

[astarmathsandphysics]

Do thety mean the cross product?

[Alpha]

Do thety mean the cross product?

No, scalar product is the dot product. They use |OA|.|OB| cos Angle= OA.OB

I checked this method. It does give you the answer. But I still don't find any logic.

[astarmathsandphysics]

I recognize this question from a p4 paper I did today. Attached.