Let `a, b and c` be distinct non-negative numbers. If vectos `a hati +a hatj +chatk, hati + hatk and chati +chatj+bhatk` are coplanar, then c is

Options

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

B

Explanation

a, b and c are distinct negative negative numbers and vectors `a hati + a hatj + chatk, hati +hatk and chati +c hatj +bhatk ` are coplanare
`" "|{:(a,,a,,c), (1,,0,,1),(c,,c,,b):}|=0`
or `ac+ c^(2) -ab -ac =0`
or `c^(2) = ab`
Hence, `a, c, b` are in G.P.
So c is the G.M. of a and b.