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Whhat are the coordinates of the vertices of a cube whose edge is 2 units, one of whose vertices coincides with the origin and the thrre edges passing thorugh the origin, coincides with the positive direction of the axes through the origin ?

Answer

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15.Write the coordinates of the vertices of a square whose each side is 5units,one vertex at (2,1) and all the vertices lie in the same quadrant.

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Knowledge Check

  • A square of side a lies above the X- axis and has one vertex at the origin . The side passing through the origin makes an angle pi//6 with the positive direction of X-axis .The equation of its diagonal not passing through the origin is

    A
    `y(sqrt(3)-1)-x(1-sqrt(3))=2a`
    B
    `y(sqrt(3)+1) +x(1-sqrt(3))=2a`
    C
    `y(sqrt(3)+1)+x(1+sqrt(3)) =2a`
    D
    `y(sqrt(3)+1)+x(sqrt(3)-1)=2a`

  • What is the equation of the circle , whose centre lies on the x-axis at a distance h from the origin and the circle passes through the origin ?

    A
    `x^(2) + y^(2)- 2hx = 0`
    B
    `x^(2) + y^(2) - 2hx + h^(2) = 0`
    C
    `x^(2) + y^(2) + 2hxy = 0`
    D
    `x^(2) + y^(2) - h^(2) = 0`

  • What is the equation of a circle whose center lies on the x-axis at a distance h from the origin and the circle passes through the origin ?

    A
    `x^(2) + y^(2) - 2hx = 0`
    B
    `x^(2) +y^(2) - 2hx + h^(2) = 0`
    C
    `x^(2) + y^(2) +2hxy = 0`
    D
    `x^(2) +y^(2) - h^(2) = 0`

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    IF veca, vecb, vecc are the position vectors of the vertices of an equilateral triangle whose orthocentre is at the origin, then

    The locus of the centre of the circle passing through the origin O and the points of intersection A and B of any line through (a, b) and the coordinate axes is

    The equation of a circle with the origin as the centre and passing through the vertices of an equilateral triangle whose altitude is of length 3 units is

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