Space geometry

9000106609

Level: 
A
Determine whether two lines are identical, parallel, intersecting or skew. The first line is the line passes through the points A=[3;−2;1] and B=[0;7;7] and the second line is the line passes through the points C=[5;−8;−3] and D=[6;−11;−5].
identical lines
parallel lines, not identical
intersecting lines
skew lines

9000106610

Level: 
A
Determine whether two lines are identical, parallel, intersecting or skew. The first line is the line passes through the points A=[1;−4;2] and B=[3;0;0] and the second line is the line passes through the points C=[3;−5;5] and D=[−1;−3;−1].
intersecting lines
parallel lines, not identical
identical lines
skew lines

1003189005

Level: 
B
We are given a straight line p by parametric equations x=1+t,y=1+2t,z=4−t; t∈R. Find the parametric equations of the line p′ that is an orthogonal projection of the line p into the coordinate xy-plane .
p′:x=5+s,y=9+2s,z=0; s∈R
p′:x=5+s,y=9−2s,z=0; s∈R
p′:x=1+s,y=1+2s,z=4; s∈R
p′:x=5+2s,y=9+s,z=0; s∈R