Maths-
General
Easy

Question

# The value of k such that lies in the plane 2x-4y+z+7=0 is

Hint:

## 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  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)=0It 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)=7Simplifying 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.