Mathematics AA: VECTORS - LINES - PLANES Topical Past Paper Questions

[Maximum mark:6] Consider the following two equations. $$ 2x+6y-8z=13 $$ $$ 3x-y+3z=12 $$ (a) Determine the general solution giving the answer in parametric form. Consider a third equation $ ax + 12y - 16z = k $, where $ a, k \in \mathbb{R} $. [2] (b) In the case where $a=3$ and…

[Maximum mark: 18] A line $L$ is defined by $L: -\frac{x}{2}+1=y+4=\frac{z}{3}$. (a) Find the equation of $L$, expressing your answer in the form $r=a+\lambda b$, where $\lambda\in\mathbb{R}$. [3] (b) Determine the minimum distance from the origin $O$ to the line $L$. [5] A plane…

[Maximum mark: 6] The following diagram shows a pyramid with vertex V and rectangular base OABC. Point B has coordinates $ (6, 8, 0) $, point C has coordinates $ (6, 0, 0) $ and point V has coordinates $ (3, 4, 9) $. diagram not to scale (a) Find BV. [2] [2] (b) Find the size of…