vectors Lines and Planes.

[Tsepiso]

I don't get part b and e of this question from the N12/5/MATHL/HP2/ENG/TZ0/XX.

how was the position vector obtained in b. and I am clueless about e.

Q13.docx

[Fiona]

Hi!

 

(b) In this part you need to find the equation of the line and, thus, solve the equations for P1 and P2 simultaneously. To do that you should equate x to t (x = t) and express y and z in terms of t. You may ask me why x = t and not y = t or z = t? Simply because they gave you a hint that the position vector for x is 0 and the direction vector -> 1 (when t is sucked out of the bracket). By equating x = t leads to this exact result. When you will find expressions for x, y and z in terms of t, that would be the equation of the line although you will need to rearrange it to make it look as in the question. (Please note that equating y to t or z to t is not wrong, you will obtain the same thing but the position vectors will be different. We did x = t to fit the result in the question).

 

Another method: Alternatively, you can equate x to 0 (x = 0) as it is already given to you that it is 0 (look at the position vector). By substituting this value of x (x = 0) into 2 equations you have will allow you to find y and z in terms of k (simply solve equations simultaneously). By doing so, you will obtain the position vector. As for direction vector, you will need to find the vector product of normals of the two planes. And only then you will be able to find the equation of the line. The result is the same as in the previous method.

 

(e) As for this part, it makes no sense. There is no such triangle. Let me check something and I will get back to you. 

[Fiona]

So, I looked at the past paper itself and here is the quote:

Let Y be a point on L1 and Z be a point on L2 such that XY is perpendicularto YZ and the area of the triangle XYZ is 3. Find the perimeter of thetriangle XYZ.

Initially, the question was typed in incorrectly, so it was not your fault that you did not get it. With such information, this part becomes pretty straightforward.

 

Here is the link to the solution of the whole question: https://www.dropbox.com/sh/zomslkqnpo6c0k3/AABaezY-CzFSZryrfs4jXoMBa?dl=0

 

Hope this helps!