Prove- A-B- A-B- 2A-B-

Consider #10; #10; ( A⃗ B⃗)× #10;(A⃗+B⃗) #10; #10; A⃗×A⃗+A⃗× #10;B⃗ B⃗×A⃗ B⃗×B⃗.........(1) #10; #10; ∵A⃗×A⃗=0 #10; #10; ...

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Multiplication with Vectors

Prove: A⃗-B...

Question

Prove: $(\to A - \to B) \times (\to A + \to B)$ = $2 (\to A \times \to B)$

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Solution

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(\to a - \to b) \times (\to a + \to b) = 2 (\to a \times \to b)

\to a

\to b

(\to a - \to b) \times [(\to b + \to a) \times (2 \to a + \to b)] = \to a + \to b

θ

\to a

\to b

| \to a | = 2, ∣ ∣ \to b ∣ ∣ = 3

∣ ∣ 2 \to a - \to b ∣ ∣ = 5,

∣ ∣ 2 \to a + \to b ∣ ∣

\to a = \frac{1}{\sqrt{10}} (3^i +^k)

\to b = \frac{1}{7} (2^i + 3^j - 6^k)

(2 \to a - \to b) \cdot [(\to a \times \to b) \times (\to a + 2 \to b)]

\to a

\to b

| \to a \times \to b |^{2} = | \to a |^{2} | \to b |^{2} - | \to a . \to b |^{2}

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