A line [MATH]m_1[/MATH] goes through the point [MATH](1,2,2)[/MATH] and is parallel to the plane x+3y+z=1 and intersects the line [MATH]m_2 : (x,y,z)=(1+t,2-2t,1+t)[/MATH].
express the equation for [MATH]m_1[/MATH] in parametric form.
Hey,
From what I know is that I need 2 points on the line [MATH]m_1[/MATH]. I know it intersects [MATH]m_2[/MATH] so If I take t=0 I get another point which is (1,2,1). Let [MATH]P_0=(1,2,2), Q=(1,2,1) \iff \vec{u}=\vec{P_0Q}=(1,2,2)-(1,2,1)=(0,0,1)[/MATH]. Now I know that [MATH]\vec{P_0Q}=t\vec{u}[/MATH]Is this correct so far? It feels like the values for my vector [MATH]\vec{u}[/MATH] are a bit odd and somehow It feels like what I did is just nonsense.
I know that it is parallel to the plane x+3y+z=1 so maybe I don´t really need to look for a vector [MATH]\vec{u}[/MATH] but instead I should use the fact that I have the equation for the plane?
express the equation for [MATH]m_1[/MATH] in parametric form.
Hey,
From what I know is that I need 2 points on the line [MATH]m_1[/MATH]. I know it intersects [MATH]m_2[/MATH] so If I take t=0 I get another point which is (1,2,1). Let [MATH]P_0=(1,2,2), Q=(1,2,1) \iff \vec{u}=\vec{P_0Q}=(1,2,2)-(1,2,1)=(0,0,1)[/MATH]. Now I know that [MATH]\vec{P_0Q}=t\vec{u}[/MATH]Is this correct so far? It feels like the values for my vector [MATH]\vec{u}[/MATH] are a bit odd and somehow It feels like what I did is just nonsense.
I know that it is parallel to the plane x+3y+z=1 so maybe I don´t really need to look for a vector [MATH]\vec{u}[/MATH] but instead I should use the fact that I have the equation for the plane?