If $p, q$ and $r$ are in A. P. then which of the following statements is correct?

p q + q r - 2 q^{2} = 0

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p q + q r - 2 p^{2} = 0

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p q + q r - p q r = 0

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p q + q r - 2 r^{2} = 0

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Solution

The correct option is C $p q + q r - 2 q^{2} = 0$
If p, q and r are in A. P., then
$p + r = 2 q$
$⟹ p + r - 2 q = 0$ multiply by q
$∴ p q + q r - 2 q^{2} = 0$

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Similar questions

⎡ ⎢ ⎣ \begin{matrix} - q r & p (q + r) & p r + p q p q + q r & - p r & p q + q r q r + p r & q r + p r & - p q \end{matrix} ⎤ ⎥ ⎦

| A |

(p q - q r + p r) (p q + q r) - (p r + p q) (p + q - r)

∠

∠

p, q, r

p + q + r = 0, a (q r + r p + p q) = 2 a - x, a p q r = y, q r = 1

△ P Q R

∠ P = 30^{0}, ∠ Q = 60^{0}, ∠ R = 90^{0}

P Q = 10

P R

Q R

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