Let a, b and c be distinct non-negative numbers. If the vectors a i + a j + c k, i + k and c i + c j + b k lie in a plane, then c is:

(A) the Geometric Mean of a and b

(B) the Arithmetic Mean of a and b

(D) the Harmonic Mean of a and b

Vector Algebra: JEE Main 2005 Mathematics question

JEE Main 2005 · Annual, Paper 1 · Q5683

JEE Main 2005Annual, Paper 1MathematicsMediumVector Algebra184× since 2002

Let

a, b

and

c

be distinct non-negative numbers. If the vectors

a\widehat i + a\widehat j + c\widehat k,\,\,\widehat i + \widehat k

and

c\widehat i + c\widehat j + b\widehat k

lie in a plane, then

c

is :

JEE Main 2005 · Annual, Paper 1 · Q5683

JEE Main 2005Annual, Paper 1MathematicsMediumVector Algebra184× since 2002

Let

a, b

and

c

be distinct non-negative numbers. If the vectors

a\widehat i + a\widehat j + c\widehat k,\,\,\widehat i + \widehat k

and

c\widehat i + c\widehat j + b\widehat k

lie in a plane, then

c

is :