Q77.If for a > 0, the feet of perpendiculars from the points A(a, −2a, 3) and B(0, 4, 5) on the plane lx + my + nz = 0 are points C(0, −a, −1) and D respectively, then the length of line segment CD is equal to : (1) √31 (2) √41 (3) √55 (4) √66
What This Question Tests
This question tests the ability to determine the equation of a plane using given information about the foot of a perpendicular, find the coordinates of another foot of perpendicular, and then calculate the distance between these two points.
Concepts Tested
Formulas Used
Vector form of line: r = a + λn
Cartesian form of line: (x-x1)/l = (y-y1)/m = (z-z1)/n
Distance between two points: √((x2-x1)² + (y2-y1)² + (z2-z1)²)
📚 NCERT Sections This Tests
2.2 — A Regular Hexagon Of Side 10 Cm Has A Charge 5 Mc At Each Of Its
Physics Class 11 · Chapter 2
2.2 A regular hexagon of side 10 cm has a charge 5 mC at each of its vertices. Calculate the potential at the centre of the hexagon.
2.3 — Two Charges 2 Mc And –2 Mc Are Placed At Points A And B 6 Cm
Physics Class 11 · Chapter 2
2.3 Two charges 2 mC and –2 mC are placed at points A and B 6 cm apart. (a) Identify an equipotential surface of the system. (b) What is the direction of the electric field at every point on this surface?
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.
📋 Question Details
- Chapter
- 3D Geometry
- Topic
- Foot of perpendicular from a point to a plane, distance between two points
- Year
- 2021
- Shift
- 16 Mar Shift 1
- Q Number
- Q77
- Type
- MCQ
- NCERT Ref
- Class 12 Mathematics Ch 11: 3D 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