Let a-b-c be distinct non-negative numbers- If the vectors a-a-bk- -k- and b-b-ck- lie in a plane- then the correct option among the following is

Since vectors are coplanar. ⇒ a amp;a amp;b 1 amp;0 amp;1 b amp;b amp;c =0 ⇒ ab a(c b)+b^2=0 ⇒ b^2=ac So, a,b,c are in G.P. ...

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Byju's Answer

Standard XII

Mathematics

Definition of a Determinant

Let a,b,c be ...

Question

Let $a, b, c$ be distinct non-negative numbers. If the vectors $a^i + a^j + b^k,^i +^k$ and $b^i + b^j + c^k$ lie in a plane, then the correct option among the following is

a, b, c

are in

A . P .

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a, b, c

are in

G . P .

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a, c, b

are in

H . P .

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a, c, b

are in

G . P .

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Solution

The correct option is B $a, b, c$ are in $G . P .$
Since vectors are coplanar.
$\Rightarrow ∣ ∣ ∣ ∣ \begin{matrix} a & a & b 1 & 0 & 1 b & b & c \end{matrix} ∣ ∣ ∣ ∣ = 0 \Rightarrow - a b - a (c - b) + b^{2} = 0 \Rightarrow b^{2} = a c$
So, $a, b, c$ are in $G . P .$

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

The correct option is B a,b,c are in G.P.Since vectors are coplanar. ⇒∣∣ ∣∣aab101bbc∣∣ ∣∣=0⇒−ab−a(c−b)+b2=0⇒b2=ac So, a,b,c are in G.P.

Let $a, b, c$ be distinct non-negative numbers. If the vectors $a^i + a^j + b^k,^i +^k$ and $b^i + b^j + c^k$ lie in a plane, then the correct option among the following is

The correct option is B $a, b, c$ are in $G . P .$
Since vectors are coplanar.
$\Rightarrow ∣ ∣ ∣ ∣ \begin{matrix} a & a & b 1 & 0 & 1 b & b & c \end{matrix} ∣ ∣ ∣ ∣ = 0 \Rightarrow - a b - a (c - b) + b^{2} = 0 \Rightarrow b^{2} = a c$
So, $a, b, c$ are in $G . P .$