1.

Let a, b and c be distinct non-negative numbers. If the vectors ahati+ahatj+c hatk, hati+hatk and chati+chatj+bhatk lie in a plane, then c is

Answer»

the HARMONIC MEAN of a and b
equal to zero
the ARITHMETIC mean of a and b
the geometric mean of a and b

Solution :SINCE , thegivenpoints lie on a plane.
`:. |{:(a,a,c),(1,0,1),(c,c,b):}| = 0`
On applying `C_(1) rarr C_(1) - C_(2)` , we get
`|{:( 0,a,c),(1,0,1),(0,c,b):}| = 0`
`rArr -1(ab - c^(2)) = 0 rArr c^(2) = ab`
Hence,c is GM of a and b.


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