Space geometry

1103189001

Level: 
B
Find the general form of the equation of the plane α that is perpendicular to the straight line p given by: x=7+t,y=2t,z=4−t; t∈R, and passes through the point A=[1;0;4]. Consequently, find the coordinates of the point B which is the point of intersection of p and α (see the picture).
α:x+2y−z+3=0; B=[6;−2;5]
α:x+2y−z−3; B=[6;−2;5]
α:x+2y−z−3=0; B=[8;2;3]
α:x+2y−z+3=0; B=[8;2;3]

1103189003

Level: 
B
Find the general form of the equation of the plane β that passes through the straight line p given by parametric equations x=1+2t,y=−2t,z=1+t; t∈R, and is perpendicular to the plane α given by x+3y−z−7=0 (see the picture).
β:x−3y−8z+7=0
β:2x−2y+z−3=0
β:x−3y−8z−7=0
β:2x−2y+z+3=0

1103189004

Level: 
B
We are given the point A=[2;−1;−4] and planes ρ by x−y+3z−5=0 and σ by 2x−y−z−8=0. Find the general form of the equation of the plane α which passes through the point A and is perpendicular to both planes (see the picture).
α:4x+7y+z+3=0
α:−2x+5y−3z−3=0
α:4x−7y+z+3=0
α:2x−5y+3z+3=0

2010008701

Level: 
B
We are given the points K=[1;−2;1], L=[2;0;−3] and the plane ρ by x−2z+3=0. Find the general form of the equation of the plane σ in which the line KL is located and is perpendicular to the plane ρ (see the picture).
σ:2x+y+z−1=0
σ:2x+3y+2z+2=0
σ:2y+z+3=0
σ:2x+y−4=0

2010008702

Level: 
B
We are given the point P=[3;−4;−5] and planes α by 2x−y−3z−5=0 and β by 3x−2y−4z+3=0. Find the general form of the equation of the plane σ which passes through the point P and is perpendicular to both planes α and β (see the picture).
σ:2x+y+z+3=0
σ:2x−y−z+15=0
σ:2x−y+z−5=0
σ:2x+y−z−7=0