1- (a) Determine as equações paramétricas da projeção da reta r: x= 3+ 3t y= -1 + t z= -3 +2t sobre o plano a : 2x - y + 2z = 1

23

n = (2,-1,2)

r = (3,1,2)

\(\[\begin{align} & e\text{ }=\text{ }r\text{ }-\text{ }p\text{ }=\text{ }\left( 3,1,2 \right)-\left( 2,-1,2 \right)\text{ }=\text{ }\left( 1,2,0 \right) \\ & 2x\text{ }-\text{ }y\text{ }+\text{ }2z\text{ }=\text{ }1 \\ & 2\left( 3+3t \right)-\left( -1+t \right)+2\left( -3+2t \right)\text{ }=\text{ }1 \\ & 9t\text{ }+\text{ }1\text{ }=\text{ }1 \\ & t\text{ }=\text{ }0 \\ & \left( 3,-1,-3 \right)\text{ } \\ & x\text{ }=\text{ }3\text{ }+\text{ }t \\ & y\text{ }=\text{ }-2\text{ }+\text{ }2t \\ & z\text{ }=\text{ }-3 \\ \end{align}\] \)