Suppose I have three planes, each of which is 'positively sloped' in the sense that the first plane intersects the x-axis at a positive value, and the y and z-axes at a negative value. Similarly, the second intersects the y-axis at a positive value, and the x and z-axes at a negative value, and the third intersects the z-axis at a positive value, and the x and y-axes at a negative value.
Will the intersection of these three planes be at the positive region? I.e., if the intersection point is $Q(x,y,z)$ are $x, y, z > 0$? The image below shows the three planes if they were orthogonal, i.e. instead of negative intersection, they never intersect the other axes. But we can tilt each plane such that they do intersect the other axes.
For the two dimensional case, if I have two lines, one intersecting x-axis at a positive value and y-axis negatively, the other intersecting y-axis positively and x-axis negatively, their point of intersection will always be in the positive quadrant, e.g. see below. I'm wondering whether this can be extended to the 3-D case?
