Distance from a plane and image in a plane

JEE Main Mathematics · 3D Geometry · 15 questions, latest first

• Let the foot of perpendicular of the point P(3,-2,-9) on the plane passing through the points (-1, -2, -3), (9, 3, 4), (9, -2, 1)…202315 April, Shift 1 · Q14
• The distance of the point (-1,2,3) from the plane r ·( i-2 j+3 k)=10 parallel to the line of the shortest distance between the…202313 April, Shift 1 · Q17
• Let the image of the point (5/3, 5/3, 8/3) in the plane x-2 y+z-2=0 be P. If the distance of the point Q(6,-2, α), α>0, from P is…202313 April, Shift 1 · Q27
• Let P be the plane passing through the points (5,3,0),(13,3,-2) and (1,6,2). For α ∈ N, if the distances of the points A(3,4, α)…202311 April, Shift 2 · Q15
• Let the line passing through the points P(2,-1,2) and Q(5,3,4) meet the plane x-y+z=4 at the point R. Then the distance of the…202311 April, Shift 2 · Q16
• Let (α, β, γ) be the image of the point P(2,3,5) in the plane 2 x+y-3 z=6. Then α+β+γ is equal to202311 April, Shift 1 · Q2
• Let the image of the point P(1,2,6) in the plane passing through the points A(1,2,0), B(1,4,1) and C(0,5,1) be Q(α, β, γ). Then…202310 April, Shift 2 · Q14
• Let the foot of perpendicular from the point A(4,3,1) on the plane P: x-y+2 z+3=0 be N. If B(5, α, β), α, β ∈ Z is a point on…202310 April, Shift 2 · Q29
• Let two vertices of a triangle ABC be (2,4,6) and ( 0,-2,-5 ), and its centroid be (2,1,-1). If the image of the third vertex in…202310 April, Shift 1 · Q13
• Let P be the plane passing through the line (x-1)/1=(y-2)/-3=(z+5)/7 and the point (2,4,-3). If the image of the point (-1,3,4)…20238 April, Shift 2 · Q13
• Let the image of the point P(1,2,3) in the plane 2 x-y+z=9 be Q. If the coordinates of the point R are (6,10,7), then the square…20236 April, Shift 1 · Q30
• Let the image of the point P(2,-1,3) in the plane x+2 y-z=0 be Q. Then the distance of the plane 3 x+2 y+z+29=0 from the point Q…20231 February, Shift 1 · Q75
• Let P be the plane, passing through the point (1,-1,-5) and perpendicular to the line joining the points (4, 1, -3) and (2, 4,…202331 January, Shift 2 · Q73
• The distance of the point (7, -3, -4) from the plane passing through the points (2, -3, 1), (-1, 1, -2) and (3,-4,2) is:202324 January, Shift 1 · Q71
• The distance of the point (-1,9,-16) from the plane 2 x+3 y-z=5 measured parallel to the line (x+4)/3=(2-y)/4=(z-3)/12 is202324 January, Shift 1 · Q76