Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
Most Important Selected Qs for JEE AdvancedMathematicsThree Dimensional Geometry

Paragraph: Let a₁ x+b₁ y+c₁ z+d₁=0 and a₂ x+b₂ y+c₂ z+d₂=0 be two planes, where d₁, d₂ 0 . Then origin lies in acute angle if a₁ a₂+b₁ b₂+c₁ c₂ 0 and origin lies in obtuse angle if a₁ a₂+b₁ b₂+c₁ c₂ 0 . Further point (x₁, y₁, z₁ ) and origin both lie either in acute angle or in obtuse angle, if (a₁ x₁+b₁ y₁+c₁ z₁+d₁ ) (a₂ x₁+b₂ y₁+c₂ z₁+d₂ ) 0 . One of (x₁, y₁, z₁ ) and origin lie in acute angle and the other in obtu

Options

  1. AO and P both lie in acute angle between the planes
  2. BO and P both lie in obtuse angle
  3. CO lies in acute angle, P lies in obtuse angle
  4. DO lies in obtuse angle, P lies an acute angle

Correct answer

B. O and P both lie in obtuse angle

Step-by-step solution

Equation of the second plane is -x+2 y-3 z+5=02(-1)+3,2+(-4)(-3) 0 origin lies in obtuse angle (2 1+3(-2)-4 3+7)(-1+2(-2)-3 3+5)=(2-6-12+7)(-1-4-9+5) 0 P lies in obtuse angle

Practice Three Dimensional Geometry on Quantrex Academy →

More from Three Dimensional Geometry

Let P be the plane such that it contains the straight line x-1 2 = y-3 3 = z+2 1 and is perpendicular to the plane x + 2y + 3z = 4 . Let P₁ be the plane which passes through the po 2026Let L be the straight line joining the points P(1, 2, -1) and Q(2, 3, 1) . Let S be the foot of the perpendicular drawn from the point R(4, -1, 5) to the line L . Another line pass 2026Let the foot of perpendicular from the point ( , 2, 3) on the line x-4 1 = y-9 2 = z-5 1 be the point (1, , 2) . Then the distance between the lines x-1 2 = y-2 3 = z+4 6 and x- 2 2026Let a line L₁ pass through the origin and be perpendicular to the lines L₂: r = (3+t) i + (2t-1) j + (2t+4) k and L₃: r = (3+2s) i + (3+2s) j + (2+s) k , t, s R . If (a, b, c) , a 2026The shortest distance between the lines x-4 1 = y-3 2 = z-2 -3 and x+2 2 = y-6 4 = z-5 -5 is : 2026Let the image of the point P(0, -5, 0) in the line x-1 2 = y 1 = z+1 -2 be the point R and the image of the point Q (0, -1 2 , 0 ) in the line x-1 -1 = y+9 4 = z+1 1 be the point S 2026Let the image of the point P(1, 6, a) in the line L: x 1 = y-1 2 = z-a+1 b , b > 0 , be ( a 3 , 0, a+c ) . If S( , , ) , > 0 , is the point on L such that the distance of S from th 2026Let a line L be perpendicular to both the lines L₁: x+1 3 = y+3 5 = z+5 7 and L₂: x-2 1 = y-4 4 = z-6 7 . If is the acute angle between the lines L and L₃: x - 8 7 2 = y - 4 7 1 = 2026 Full Three Dimensional Geometry list All Most Important Selected Qs for JEE Advanced PYQs