For any 3 vectors a b and c prove that - a - b b - c c - a - - 2- a b c -

[ Since, ( a⃗ +b⃗ #160; ) ×( b⃗ +c⃗ #160; ) =a⃗×b⃗ +a⃗×c⃗ #160;; Now, let E=[ a⃗ +b⃗ ...

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Addition of Vectors

For any 3 vec...

Question

For any 3 vectors $\to a \to b$ and $\to c$ prove that
$[\to a + \to b \to b + \to c \to c + \to a] = 2 [\to a \to b \to c]$

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Solution

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\to a, \to b, \to c; ∣ ∣ ∣ (\to a \times \to b) \cdot \to c ∣ ∣ ∣ = ∣ ∣ \to a ∣ ∣ ∣ ∣ ∣ \to b ∣ ∣ ∣ ∣ ∣ \to c ∣ ∣

[\to a + \to b \to b + \to c \to c + \to a] = λ_{1} [\to a \to b \to c]

[\to a \times \to b \to b \times \to c \to c \times \to a] = [\to a \to b \to c]^{λ_{2}}

\frac{λ_{1} + λ_{2}}{3}

\to a, \to b, \to c

L e t \to a =^i -^j, \to b =^j -^k, \to c =^k -^i .

\to d

\to a \cdot \to d = 0 = [\to b \to c \to d],

\to d

(\to A + \to B) . (\to A - \to B) = 0 t h e n \to A : \to B

[\to a - \to b \to b - \to c \to c - \to a]

| \to a | = 1, | \to b | = 5, | \to c | = 3

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