Paper 3 October/November 2011 MATHEMATICS (9709/31) A Levels
لطفا برای اطمینان از عملکرد و تجربه بهتر از مرورگرهای مدرن و به روز مانند کروم یا فایرفاکس استفاده کنید.

The straight line $l$ has equation $r = 2i - j - 4k + \lambda \left( {i + 2j + 2k} \right)$. The plane $p$ has equation $3x - y + 2z = 9$.
The line $l$ intersects the plane $p$ at the point $A$.
a) Find the position vector of $A$.
b) Find the acute angle between $l$ and $p$.
c) Find an equation for the plane which contains $l$ and is perpendicular to $p$, giving your answer in the form $\alpha x + by + cz = d$.