Science:Math Exam Resources/Courses/MATH152/April 2015/Question B 3 (a)/Statement

Line $l_{1}$ and plane $P_{1}$ shown in the figure are given in parametric form as

$l_{1}:\mathbf {x} =t\mathbf {a} ,\quad P_{1}:\mathbf {x} =\mathbf {q} +s_{1}\mathbf {b} _{1}+s_{2}\mathbf {b} _{2},$

where

$\mathbf {a} ={\begin{bmatrix}0\\1\\2\end{bmatrix}},\quad \mathbf {q} ={\begin{bmatrix}1\\1\\1\end{bmatrix}},\quad \mathbf {b} _{1}={\begin{bmatrix}0\\1\\0\end{bmatrix}},\quad \mathbf {b} _{2}={\begin{bmatrix}1\\2\\-1\end{bmatrix}}.$

(a) Find the intersection point of the line $l_{1}$ and plane $P_{1}$.