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Let \(a,b\) and \(c\) be the distinct non-negative numbers. If the vectors \(a\hat{i}+a\hat{j}+c\hat{k},\text{ }\hat{i}\…

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Let \(a,b\) and \(c\) be the distinct non-negative numbers. If the vectors \(a\hat{i}+a\hat{j}+c\hat{k},\text{ }\hat{i}\text{ }+\text{ }\hat{k}\text{ , }c\hat{i}\text{ }+\text{ }c\hat{j}+b\hat{k}\) lie on a plane, then which one of the following is correct?

a

c is the arithmetic mean of a and b

b

c is the geometric mean of a and b

c

c is the harmonic mean of a and b

d

c is equal to zero

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