3. Consider the two lines L: r = +t and L2: r = < 2,0,2>+s...

 

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3. Consider the two lines L: r = <1,1,0>+t <1,-1,2> and L2: r = < 2,0,2>+s . (a) Show that the line L1 and L2 intersect and find the intersection point. (b) Find the parametric equations for the line that is perpendicular to L1 and L2 and passes through the intersection point of L1 and L2. (c) Find an equation of the plane determined by the lines L1 and L2. 4. (a) Where does the line through (1,0, 1) and (4, -2, 2) intersect the plane x+y+2=6? (b) Find a symmetric equation of the line through (5,0,2), which is parallel to the planes x-4y+22=0 and 22x+3y-2+1=0. 3. Consider the two lines L: r = <1,1,0>+t <1,-1,2> and L2: r = < 2,0,2>+s . (a) Show that the line L1 and L2 intersect and find the intersection point. (b) Find the parametric equations for the line that is perpendicular to L1 and L2 and passes through the intersection point of L1 and L2. (c) Find an equation of the plane determined by the lines L1 and L2. 4. (a) Where does the line through (1,0, 1) and (4, -2, 2) intersect the plane x+y+2=6? (b) Find a symmetric equation of the line through (5,0,2), which is parallel to the planes x-4y+22=0 and 22x+3y-2+1=0.

Answer rating: 100% (QA)

a To show that the lines L and L intersect we need to find the values of t and s for which the equations of the lines are satisfied simultaneously The ... View the full answer