Question

Let a, b, c be distinct non – negative numbers. If the vectors $a\hat{i}+a\hat{j}+c\hat{k},\hat{i}+\hat{k}$ and $c\hat{i}+c\hat{j}+b\hat{k}$ lie in a plane, then c is

• A. the arithmetic mean of a and b
• B. the geometric mean of a and b
• C. the harmonic mean of a and b
• D. equal to zero

Answer 1

The correct option is B the geometric mean of a and b

For lying in the same plane
$\left[\overrightarrow{a}\overrightarrow{b}\overrightarrow{c}\right]=0$