Q88.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, 3). Then the distance of P from the point (3, −2, 2) is (1) 6 (2) 4 (3) 5 (4) 7
What This Question Tests
This is a direct application of formulas for finding the equation of a plane given a point and its normal vector (derived from the line joining two points) and subsequently calculating the distance of another point from this plane.
Concepts Tested
Formulas Used
Equation of plane: A(x-x_0) + B(y-y_0) + C(z-z_0) = 0
Distance = |Ax_1 + By_1 + Cz_1 + D| / √(A² + B² + C²)
📚 NCERT Sections This Tests
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.
2.5 — A Parallel Plate Capacitor With Air Between The Plates Has A
Physics Class 11 · Chapter 2
2.5 A parallel plate capacitor with air between the plates has a capacitance of 8 pF (1pF = 10–12 F). What will be the capacitance if the distance between the plates is reduced by half, and the space between them is filled with a substance of dielectric constant 6?
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.
📋 Question Details
- Chapter
- 3D Geometry
- Topic
- Planes
- Year
- 2023
- Shift
- 31 Jan Shift 2
- Q Number
- Q88
- Type
- MCQ
- 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