If the vectors - ai-aj-ck- - i-k- - - ci-cj-bk are coplanar- then prove that c is the geometric mean of a and b-

Since α, β, γ are coplanar vectors.Therefore, [α β γ]=0 a amp; a amp; c 1 amp; 0 amp; 1 c amp; c amp; b = 0 a ...

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Perimeter of a Triangle

If the vector...

Question

If the vectors $\to α = a ˆ i + a ˆ j + c ˆ k, \to β = ˆ i + ˆ k, γ = c ˆ i + c ˆ j + b ˆ k$ are coplanar, then prove that c is the geometric mean of a and b.

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a ¯ i + a ¯ j + c ¯ ¯ ¯ k, ¯ i + ¯ ¯ ¯ k, c ¯ i + c ¯ j + b ¯ ¯ ¯ k

C

a, b

c

a ˆ i + a ˆ j + c ˆ k, ˆ i + ˆ k

c ˆ i + c ˆ j + b ˆ k

c

a i + a j + c k +, i + k

c i + c j + b k

a, b

c

a i + a j + c k, i + k

c i + c j + b k

c

1

\to l = a ¯ i + b ¯ j + c ¯ ¯ ¯ k, \to m = b ¯ i + c ¯ j + a ¯ ¯ ¯ k

\to n = c ¯ i + a ¯ j + b ¯ ¯ ¯ k

a, b, c

a = b = c

2

l \to a + m \to b + n \to c = \to 0

l, m, n

\to a

\to b

\to c

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