Home
Class 12
MATHS
Consider a pyramid OPQRS located in the ...

Consider a pyramid OPQRS located in the first octant `(xge0, yge0, zge0)` with O as origin and OP and OR along the X-axis and the Y-axis , respectively. The base OPQRS of the pyramid is a square with OP=3. The point S is directly above the mid point T of diagonal OQ such that TS=3. Then,

A

the acute angle between OQ and OS is `(pi)/(3)`

B

the equation of the plane containing ht `triangleOQS` is x-y=0

C

the length of perpendicular from P to the plane containing the `triangleOQS` is `(2)/(sqrt(3))`

D

the perpendicular distance from O to the straight line containing RS is `sqrt((15)/(2))`

Text Solution

Verified by Experts

The correct Answer is:
`(b,c, d)`
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • THREE DIMENSIONAL COORDINATE SYSTEM

    ARIHANT MATHS ENGLISH|Exercise Three Dimensional Coordinate System Exercise 12 : Question Asked in Previous Years Exam|2 Videos
  • THREE DIMENSIONAL COORDINATE SYSTEM

    ARIHANT MATHS ENGLISH|Exercise Three Dimensional Coordinate System Exercise 11 : Subjective Type Questions|1 Videos
  • THEORY OF EQUATIONS

    ARIHANT MATHS ENGLISH|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|35 Videos
  • TRIGONOMETRIC EQUATIONS AND INEQUATIONS

    ARIHANT MATHS ENGLISH|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|12 Videos

Similar Questions

Explore conceptually related problems

Consider the cube in the first octant with sides OP,OQ and OR of length 1, along the x-axis, y-axis and z-axis, respectively, where O(0,0,0) is the origin. Let S(1/2,1/2,1/2) be the centre of the cube and T be the vertex of the cube opposite to the origin O such that S lies on the diagonal OT. If vec(p)=vec(SP), vec(q)=vec(SQ), vec(r)=vec(SR) and vec(t)=vec(ST) then the value of |(vec(p)xxvec(q))xx(vec(r)xx(vect))| is

A circle touching the X-axis at (3, 0) and making a intercept of length 8 on the Y-axis passes through the point

Knowledge Check

  • The graph of y^4-3x^2+7=0 is symmetric with respect to which of the following? the x-axis the y-axis the origin

    A
    only I
    B
    only II
    C
    only III
    D
    I, II, and III
  • Similar Questions

    Explore conceptually related problems

    Two point charge -q and +q//2 are situated at the origin and the point (a,0,0) respectively. The point along the X -axis where the electic field Vanishes is

    In the figure, two point charges +q and -q are placed on the x-axis at (+a,0) and (-a,0) respectively. A tiny dipole of dipolem moment (p) is kept at the origin along the y-axis. The torque on the dipole equals

    Find the points on the curve x^2+y^2-2x-3=0 at which the tangents are parallel to the x-axis and y-axis.

    If the point 3x+4y-24=0 intersects the X -axis at the point A and the Y -axis at the point B , then the incentre of the triangle OAB , where O is the origin, is

    In the figure, OA and OB are two uniformly charged wires, placed along x and y axis respectively. Find the unit vector in the direction of field at point (0,0,sqrt(3L)) .

    Find the points on the curve x^2+y^2-2x-3=0 at which the tangents are parallel to the x-axis.

    Consider two positive point charges, each of magnitude q, placed on the y-axis at the points (0, a) and (0, -a). A positively charged particle of charge q' and mass m is displaced slightly from the origin in the direction of the positive x-axis. Speed of charge q' at infinity is