Space geometry

2010008901

Level: 
A
Given points K=[−3;1;5] and L=[1;−5;4], determine which of the following parametric equations does not define the ray KL.
↦KL:x=−3+4t,y=1−6t,z=5−t; t∈(−∞;0]
↦KL:x=−3+4t,y=1−6t,z=5−t; t∈[0;∞)
↦KL:x=−3−8t,y=1+12t,z=5+2t; t∈(−∞;0]
↦KL:x=−3+8t,y=1−12t,z=5−2t; t∈[0;∞)

2010008902

Level: 
A
Given points A=[−2;5;1] and B=[3;−1;2], determine which of the following parametric equations defines the ray AB.
↦AB:x=3+5t,y=−1−6t,z=2+t; t∈[−1;∞)
↦AB:x=−2+5t,y=5−6t,z=1+t; t∈(−∞;1]
↦AB:x=3−5t,y=−1+6t,z=2−t; t∈(−∞;0]
↦AB:x=−2−5t,y=5+6t,z=1−t; t∈[0;∞)

2010008903

Level: 
A
Given points P=[3;−4;1] and Q=[−1;3;6], determine which of the following parametric equations defines the ray QP.
↦QP:x=−1−4t,y=3+7t,z=6+5t; t∈(−∞;0]
↦QP:x=3−4t,y=−4+7t,z=1+5t; t∈[−1;∞)
↦QP:x=3+4t,y=−4−7t,z=1−5t; t∈[0;∞)
↦QP:x=−1+4t,y=3−7t,z=6−5t; t∈(−∞;1]

2010008904

Level: 
A
We are given points K=[4;0;3], L=[1;−3;2] and M=[2;2;0]. From the following list, choose the parametric equations which represent a plane σ defined by the points K, L, and M.
σ:x=1+3r+s,y=−3+3r+5s,z=2+r−2s; r,s∈R
σ:x=1−3r−s,y=−3+3r−5s,z=2+r+2s; r,s∈R
σ:x=1−3r+s,y=−3−3r+5s,z=2+r−2s; r,s∈R
σ:x=1+3r+s,y=−3+3r−5s,z=2−r+2s; r,s∈R