Q89.Consider a line L passing through the points P(1, 2, 1) and Q(2, 1, −1). If the mirror image of the point A(2, 2, 2) in the line L is (α, β, γ), then α + β + 6γ is equal to _______
What This Question Tests
This question tests the ability to find the mirror image of a point with respect to a line in 3D space, which involves finding the foot of the perpendicular and using the midpoint formula.
Concepts Tested
Formulas Used
Line equation: (x-x₁)/a = (y-y₁)/b = (z-z₁)/c = λ
Dot product for perpendicularity: a₁a₂ + b₁b₂ + c₁c₂ = 0
Midpoint formula: ((x₁+x₂)/2, (y₁+y₂)/2, (z₁+z₂)/2)
📚 NCERT Sections This Tests
9.15 — Apply Mirror Equation And The Condition:
Physics Class 12 · Chapter 9
9.15 Apply mirror equation and the condition: (a) f < 0 (concave mirror); u < 0 (object on left) (b) f > 0; u < 0 (c) f > 0 (convex mirror) and u < 0 (d) f < 0 (concave mirror); f < u < 0 to deduce the desired result.
2.1 — Two Charges 5 × 10–8 C And –3 × 10–8 C Are Located 16 Cm Apart. At
Physics Class 11 · Chapter 2
2.1 Two charges 5 × 10–8 C and –3 × 10–8 C are located 16 cm apart. At what point(s) on the line joining the two charges is the electric potential zero? Take the potential at infinity to be zero.
9.1 — A Small Candle, 2.5 Cm In Size Is Placed At 27 Cm In Front Of A Concave
Physics Class 12 · Chapter 9
9.1 A small candle, 2.5 cm in size is placed at 27 cm in front of a concave mirror of radius of curvature 36 cm. At what distance from the mirror should a screen be placed in order to obtain a sharp image? Describe the nature and size of the image. If the candle is moved closer to the mirror, how would the screen have to be moved?
📋 Question Details
- Chapter
- 3D Geometry
- Topic
- Mirror image of a point in a line
- Year
- 2024
- Shift
- 04 Apr Shift 2
- Q Number
- Q89
- Type
- Numerical
- NCERT Ref
- Class 12 Mathematics Ch 11: Three Dimensional Geometry
More from this Chapter
Q88.The projections of a vector on the three coordinate axis are 6, −3, 2 respectively. The direction cosines of the vector are (1) 6, −3, 2 (2) 65 , −35 , 25 (3) 7 6 , −37 , 27 (4) −67 , −37 , 27
Q87.Statement-1: The point A(3, 1, 6) is the mirror image of the point B(1, 3, 4) in the plane x −y + z = 5. Statement-2: The plane x −y + z = 5 bisects the line segment joining A(3, 1, 6) and B(1, 3, 4). (1) Statement-1 is true, Statement-2 is true; (2) Statement-1 is true, Statement-2 is false Statement-2 is not the correct explanation for Statement-1 (3) Statement-1 is false, Statement-2 is true (4) Statement-1 is true, Statement-2 is true; Statement-2 is the correct explanation for Statement-1 JEE Main 2010 JEE Main Previous Year Paper
Q88.A line AB in three-dimensional space makes angles 45∘ and 120∘ with the positive x-axis and the positive y- axis respectively. If AB makes an acute angle θ with the positive z-axis, then θ equals (1) 45∘ (2) 60∘ (3) 75∘ (4) 30∘
Q87.If the angle between the line x = y−12 = 14 (√5 ) (1) 3 (2) 2 2 5 (3) 5 (4) 2 3 3