A sphere of radius 1m has an equation of the form x2+y2+z2=r2
Statement 1: For its surface, only 6 distinct numbers of normal vectors are possible.
Statement 2: At every point of its surface intersecting with the coordinate Axis, there will a normal vector along the direction of coordinate axis at those points.
A sphere of radius 1m has an equation of the form x2+y2+z2=r2
Statement 1: For its surface, only 6 distinct numbers of normal vectors are possible.
Statement 2: At every point of its surface intersecting with the coordinate Axis, there will a normal vector along the direction of coordinate axis at those points.
The correct option is D 1 is false 2 is true
The given equation x2+y2+z2=r2 , as you would have learned in basic coordinate geometry, is the three dimensional equation of a sphere centered at origin and of radius ‘r’.
You must agree that it is obviously a non-planar surface and a common normal for the entire surface cannot be defined.
One can only define a normal for elementary parts of its surface. Now the surface can be broken down into infinite infinitesimal parts. Do you concur? If not take a look at this figure-
Therefore infinite number of normal vectors are possible, implies statement 1 is wrong.
Consider the normal vector at infinitesimal parts on the surface of the sphere intersecting with the coordinate axis as shown,
At these points each normal vector will point along the axes, take point A as an example.
Thus 6 such vectors are possible and statement 2 is correct.
1 is false 2 is true
The given equation x2+y2+z2=r2 , as you would have learned in basic coordinate geometry, is the three dimensional equation of a sphere centered at origin and of radius ‘r’.
You must agree that it is obviously a non-planar surface and a common normal for the entire surface cannot be defined.
One can only define a normal for elementary parts of its surface. Now the surface can be broken down into infinite infinitesimal parts. Do you concur? If not take a look at this figure-
Therefore infinite number of normal vectors are possible, implies statement 1 is wrong.
Consider the normal vector at infinitesimal parts on the surface of the sphere intersecting with the coordinate axis as shown,
At these points each normal vector will point along the axes, take point A as an example.
Thus 6 such vectors are possible and statement 2 is correct.
