Most vaccines protect only against pathogens that fall within a certain region i

Question

Most vaccines protect only against pathogens that fall within a certain region in antigenic space. Suppose that a vaccine protects against any strain falling within a sphere with equation, x'+(y-3)+(z-1-4 in antigenic space. Identify which of the following strains, located in antigenic space, this vaccine will be effective against. A. A strain located at (1,1,1) in antigenic space. B. A strain located at (0,1.5,1) in antigenic space. ° C. A strain located at (0,0,0) in antigenic space. D. A strain located at (1,0,1) in antigenic space.

Explanation / Answer

Answer to the above question is:

This is a sphere equation with radius 2 and centered at (0,3,1)

Basically this equation covers a radius of 2 meters, within which this vaccine is effective against diseases.

So, lets calculate distance of center of spehere wr.t to all points in options and conclude whether they are smaller than 2 or not:

distance =(0-1)^2 + (3-1)^2 + (1-1)^2 = 5
radial =sqrt(5) which is more than 2
So, A is not correct

distance =(0-0)^2 + (3-1.5)^2 + (1-1)^2 = 2.25
radial =sqrt(2.25) which is less than 2
So, B is correct

distance =(0-0)^2 + (3-0)^2 + (1-0)^2 = 10
radial =sqrt(10) which is more than 2
So, C is not correct

distance =(0-1)^2 + (3-0)^2 + (1-1)^2 = 10
radial =sqrt(10) which is more than 2
So, D is not correct

B is correct option

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