Maths-
General
Easy

Question

The value of k such that fraction numerator x minus 4 over denominator 1 end fraction equals fraction numerator y minus 2 over denominator 1 end fraction equals fraction numerator z minus k over denominator 2 end fraction lies in the plane 2x-4y+z+7=0 is

  1. 7    
  2. -7    
  3. 4    
  4. no value    

Hint:

The study of shapes in three dimensions using the three coordinates of x, y, and z is known as three-dimensional geometry. Finding a point's precise placement in a 3D space requires the input of three parameters. Here we have given fraction numerator x minus 4 over denominator 1 end fraction equals fraction numerator y minus 2 over denominator 1 end fraction equals fraction numerator z minus k over denominator 2 end fraction lies in the plane 2x-4y+z+7=0, we have to find the value of k.

The correct answer is: -7


    In three-dimensional geometry, the term "coordinate system" refers to the method of locating a point in the coordinate plane. There is a common place where three parallel lines cross. The three lines are the axes, and that shared point is known as the origin.
    They are, in order, the x-axis, y-axis, and z-axis. O is the observer in relation to the measurement of any other point from his position.
    Here we have given n fraction numerator x minus 4 over denominator 1 end fraction equals fraction numerator y minus 2 over denominator 1 end fraction equals fraction numerator z minus k over denominator 2 end fraction lies in the plane 2x-4y+z+7=0.
    Lets put (1,1,2) in the given equation, we get:
    2(1)-4(1)+(2)=0
    It shows that line is parallel to the given plane. Only if the point (4,2,k) also lies on the plane will it now be in the plane.
    We have given that the line passes through the the points (4,2,k), so putting the points in the equation, we get:
    2(4)-4(2)+(k)=7
    Simplifying it, we get:
    k=7

    So here we used the concept of three dimensional geometry to understand and solve the question. Any point's position or coordinates in 3D space are determined by how far they have travelled along the x, y, and z axes, respectively. So here the value of k is 7.

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