aq−raq−r\frac{a}{{q - r}} = br−p" role="presentation">br−pbr−p\frac{b}{{r - p}} = cp−q," role="presentation">cp−q,cp−q,\frac{c}{{p - q}}{\text{,}} find the value of pa + qb + rc is?" /> aq−raq−r\frac{a}{{q - r}} = br−p" role="presentation">br−pbr−p\frac{b}{{r - p}} = cp−q," role="presentation">cp−q,cp−q,\frac{c}{{p - q}}{\text{,}} find the value of pa + qb + rc is?" /> aq−raq−r\frac{a}{{q - r}} = br−p" role="presentation">br−pbr−p\frac{b}{{r - p}} = cp−q," role="presentation">cp−q,cp−q,\frac{c}{{p - q}}{\text{,}} find the value of pa + qb + rc is?" />

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If $\frac{a}{q - r}$ $\frac{a}{{q - r}}$ = $\frac{b}{r - p}$ $\frac{b}{{r - p}}$ = $\frac{c}{p - q},$ $\frac{c}{{p - q}}{\text{,}}$ find the value of pa + qb + rc is?

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Answer:- 1

Explanation:-

Solution:

\begin{aligned} Let \frac{a}{q - r} = \frac{b}{r - p} = \frac{c}{p - q} = k \\ \frac{a}{q - r} = k (On multiplying by p) \\ p a = k (p q - p r) . . . . . . (i) \\ In the same way we can write \\ qb = k (q r - q p) . . . . . . . . (i i) \\ And r c = k (r p - r p) . . . . . i i i) \\ On adding equation (i), (ii) and (iii) \\ p a + q b + r c \\ = k (p q - p r + q r - q p + r p - r q) \\ = 0 \end{aligned}

$\eqalign{ & {\text{Let }}\frac{a}{{q - r}} = \frac{b}{{r - p}} = \frac{c}{{p - q}} = k \cr & \frac{a}{{q - r}} = k{\text{ }}\left( {{\text{On multiplying by }}p} \right) \cr & pa = k\left( {pq - pr} \right)\,......(i) \cr & {\text{In the same way we can write}} \cr & {\text{qb = k}}\left( {qr - qp} \right)\,........(ii) \cr & {\text{And }}rc = k\left( {rp - rp} \right)\,.....iii) \cr & {\text{On adding equation (i), (ii) and (iii) }} \cr & pa + qb + rc \cr & = k\left( {pq - pr + qr - qp + rp - rq} \right) \cr & = 0 \cr}$

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=

\frac{b}{r - p}

$\frac{b}{{r - p}}$ =

\frac{c}{p - q},

$\frac{c}{{p - q}}{\text{,}}$ find the value of pa + qb + rc is?", "text": "If

\frac{a}{q - r}

$\frac{a}{{q - r}}$ =

\frac{b}{r - p}

$\frac{b}{{r - p}}$ =

\frac{c}{p - q},

$\frac{c}{{p - q}}{\text{,}}$ find the value of pa + qb + rc is?", "dateCreated": "7/24/2019 10:09:12 AM", "author": { "@type": "Person", "name": "Nitin Sir" }, "answerCount": "4", "acceptedAnswer": { "@type": "Answer", "text": "

Solution:

\begin{aligned} Let \frac{a}{q - r} = \frac{b}{r - p} = \frac{c}{p - q} = k \\ \frac{a}{q - r} = k (On multiplying by p) \\ p a = k (p q - p r) . . . . . . (i) \\ In the same way we can write \\ qb = k (q r - q p) . . . . . . . . (i i) \\ And r c = k (r p - r p) . . . . . i i i) \\ On adding equation (i), (ii) and (iii) \\ p a + q b + r c \\ = k (p q - p r + q r - q p + r p - r q) \\ = 0 \end{aligned}

$\eqalign{ & {\text{Let }}\frac{a}{{q - r}} = \frac{b}{{r - p}} = \frac{c}{{p - q}} = k \cr & \frac{a}{{q - r}} = k{\text{ }}\left( {{\text{On multiplying by }}p} \right) \cr & pa = k\left( {pq - pr} \right)\,......(i) \cr & {\text{In the same way we can write}} \cr & {\text{qb = k}}\left( {qr - qp} \right)\,........(ii) \cr & {\text{And }}rc = k\left( {rp - rp} \right)\,.....iii) \cr & {\text{On adding equation (i), (ii) and (iii) }} \cr & pa + qb + rc \cr & = k\left( {pq - pr + qr - qp + rp - rq} \right) \cr & = 0 \cr}$ ", "dateCreated": "7/24/2019 10:09:12 AM", "author": { "@type": "Person", "name": "Nitin Sir" } }, "suggestedAnswer": { "@type": "Answer", "text": "

Solution:

\begin{aligned} Let \frac{a}{q - r} = \frac{b}{r - p} = \frac{c}{p - q} = k \\ \frac{a}{q - r} = k (On multiplying by p) \\ p a = k (p q - p r) . . . . . . (i) \\ In the same way we can write \\ qb = k (q r - q p) . . . . . . . . (i i) \\ And r c = k (r p - r p) . . . . . i i i) \\ On adding equation (i), (ii) and (iii) \\ p a + q b + r c \\ = k (p q - p r + q r - q p + r p - r q) \\ = 0 \end{aligned}

$\eqalign{ & {\text{Let }}\frac{a}{{q - r}} = \frac{b}{{r - p}} = \frac{c}{{p - q}} = k \cr & \frac{a}{{q - r}} = k{\text{ }}\left( {{\text{On multiplying by }}p} \right) \cr & pa = k\left( {pq - pr} \right)\,......(i) \cr & {\text{In the same way we can write}} \cr & {\text{qb = k}}\left( {qr - qp} \right)\,........(ii) \cr & {\text{And }}rc = k\left( {rp - rp} \right)\,.....iii) \cr & {\text{On adding equation (i), (ii) and (iii) }} \cr & pa + qb + rc \cr & = k\left( {pq - pr + qr - qp + rp - rq} \right) \cr & = 0 \cr}$ ", "dateCreated": "7/24/2019 10:09:12 AM" } }

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