Question

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

• A. A.M. of a and b
• B. G.M. of a and b
• C. H.M of a and b
• D. Equal to zero

Answer 1

Answer: (B)

G.M. of a and b

Answer 2

Since these vectors are coplaner, =0

⇒ -ac – a( b –c) + c² = 0 ⇒ c² = ab