Prove That B C 2 A 2 A 2 B 2 C A 2 B 2 C 2 C 2 A B 2 2abc A

Prove That 2a 2 2b 2 2c 2 2ab 2bc 2ac A B 2 B C 2 C A 2 Using properties of determinants prove that: |((b c)^2, ab, ca)(ab, (a b)^2, bc)(ac, bc, (a b)^2) =2abc (a b c)^3. To ask unlimited maths doubts download doubtnut from goo.gl 9wzjcw prove that `| ((b c)^2, a^2,a^2),(b^2,(c a)^2,b^2),(c^2,c^2,(a b)^2)|=2abc(a b c.

Prove That B C 2 A 2 A 2 B 2 C A 2 B 2 2abc A B C 3 C To prove that (b c), (c a), and (a b) are in arithmetic progression (a.p.), we will use the given information that (b c)^2, (c a)^2, and (a b)^2 are in a.p. we will break down the proof into the following sections: 1. let (b c)^2 be the first term of the a.p., (c a)^2 be the second term, and (a b)^2 be the third term. 2. If $a^2,b^2,c^2$ are in arithmetic progression, prove that $b c,c a,a b$ are in harmonic progression. first, an implicit assumption is that $\,(b c)(c a)(a b)\ne 0.\,$ notice that $\,a,b,c\,$ are in a.p. is equivalent to $\,a 2b c=0.\,$. If \[a\left( \frac{1}{b} \frac{1}{c} \right), b\left( \frac{1}{c} \frac{1}{a} \right), c\left( \frac{1}{a} \frac{1}{b} \right)\] are in a.p., prove that a, b, c are in a.p. a man saves rs 32 during the first year. Supplementary example 6 for any three vectors ∴ 𝑎 ⃗, 𝑏 ⃗, and 𝑐 ⃗, prove that [ 8(𝑎 ⃗" " 𝑏 ⃗&𝑏 ⃗ 𝑐 ⃗&𝑐 ⃗ 𝑎 ⃗ )] = 2 [𝑎 ⃗ , 𝑏 ⃗, 𝑐 ⃗] to prove [ 8(𝑎 ⃗" " 𝑏 ⃗&𝑏 ⃗ 𝑐 ⃗&𝑐 ⃗ 𝑎 ⃗ )] = 2 [𝑎 ⃗ , 𝑏 ⃗, 𝑐 ⃗] solving lhs [ 8(𝑎 ⃗" " 𝑏 ⃗.

Prove That B C 2 A 2 A 2 B 2 C A 2 B 2 C 2 C 2 A B 2 2abc A If \[a\left( \frac{1}{b} \frac{1}{c} \right), b\left( \frac{1}{c} \frac{1}{a} \right), c\left( \frac{1}{a} \frac{1}{b} \right)\] are in a.p., prove that a, b, c are in a.p. a man saves rs 32 during the first year. Supplementary example 6 for any three vectors ∴ 𝑎 ⃗, 𝑏 ⃗, and 𝑐 ⃗, prove that [ 8(𝑎 ⃗" " 𝑏 ⃗&𝑏 ⃗ 𝑐 ⃗&𝑐 ⃗ 𝑎 ⃗ )] = 2 [𝑎 ⃗ , 𝑏 ⃗, 𝑐 ⃗] to prove [ 8(𝑎 ⃗" " 𝑏 ⃗&𝑏 ⃗ 𝑐 ⃗&𝑐 ⃗ 𝑎 ⃗ )] = 2 [𝑎 ⃗ , 𝑏 ⃗, 𝑐 ⃗] solving lhs [ 8(𝑎 ⃗" " 𝑏 ⃗. Recall that the value of a determinant remains same if we apply the operation ri→ ri krj or ci→ ci kcj. expanding the determinant along r1, we have. Δ = 0 (2c2) [ (b2) (a2 b2 – c2)] (–2b2) [– (c2) (c2 a2 – b2)] ⇒ Δ = 2b2c2(a2 b2 – c2) 2b 2c 2 (c2 a2 – b2) ⇒ Δ = 2b2c2 [ (a2 b2 – c2) (c2 a2 – b2)] ⇒ Δ = 2b2c2[2a2] ∴ Δ = 4a2b2c. If a, b and c are in continued proportion, prove that a 2 b 2 c 2 (a b c) 2 = a b c a b c. given, a, b and c are in continued proportion. therefore, a b = b c. ac = b 2. l.h.s = a 2 b 2 c 2 (a b c) 2. = a 2 b 2 c 2 2 a b 2 b c 2 a c (2 a b 2 b c 2 a c) (a b c) 2. To ask unlimited maths doubts download doubtnut from goo.gl 9wzjcw prove that in any triangle abc(i) `c^2 = a^2 b^2 2ab cos c` (ii) `c=bcosa acosb`. If a, b, c are the roots of x 3 q x r = 0, form the equation whose roots are b 2 c 2, c 2 a 2, a 2 b 2.

Prove That Determinant B C 2a2 A2 B2 C A 2 B2 2abc A B C 3 C2 C2 A Recall that the value of a determinant remains same if we apply the operation ri→ ri krj or ci→ ci kcj. expanding the determinant along r1, we have. Δ = 0 (2c2) [ (b2) (a2 b2 – c2)] (–2b2) [– (c2) (c2 a2 – b2)] ⇒ Δ = 2b2c2(a2 b2 – c2) 2b 2c 2 (c2 a2 – b2) ⇒ Δ = 2b2c2 [ (a2 b2 – c2) (c2 a2 – b2)] ⇒ Δ = 2b2c2[2a2] ∴ Δ = 4a2b2c. If a, b and c are in continued proportion, prove that a 2 b 2 c 2 (a b c) 2 = a b c a b c. given, a, b and c are in continued proportion. therefore, a b = b c. ac = b 2. l.h.s = a 2 b 2 c 2 (a b c) 2. = a 2 b 2 c 2 2 a b 2 b c 2 a c (2 a b 2 b c 2 a c) (a b c) 2. To ask unlimited maths doubts download doubtnut from goo.gl 9wzjcw prove that in any triangle abc(i) `c^2 = a^2 b^2 2ab cos c` (ii) `c=bcosa acosb`. If a, b, c are the roots of x 3 q x r = 0, form the equation whose roots are b 2 c 2, c 2 a 2, a 2 b 2.

Prove That A 2 B 2 C 2 Ab Bc Ca 1 2 A B 2 B C 2 C A To ask unlimited maths doubts download doubtnut from goo.gl 9wzjcw prove that in any triangle abc(i) `c^2 = a^2 b^2 2ab cos c` (ii) `c=bcosa acosb`. If a, b, c are the roots of x 3 q x r = 0, form the equation whose roots are b 2 c 2, c 2 a 2, a 2 b 2.

Prove The Following A 2 Bc Ac C 2 A 2 Ab B 2 Ac Ab B 2 Bc C 2