Evaluate the product 3a-5b- 2a-7b- -

(3a⃗ 5b⃗)· (2a⃗+7b⃗) =3a⃗· 2a⃗+3a⃗· 7b⃗ 5b⃗· 2a⃗ 5b⃗· 7b⃗ =6a⃗· #160;a⃗+21a⃗· #160;b⃗ 10a⃗· #160;b⃗ 35b⃗· #160;b⃗ =6|a⃗|^2+11a⃗· #160;b ...

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Sum of Infinite Terms of a GP

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Question

Evaluate the product $(3 \to a - 5 \to b) \cdot (2 \to a + 7 \to b)$ .

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Solution

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(3 \to a - 5 \to b) \cdot (2 \to a - 7 \to b)

\to a

\to b

| \to a + \to b | = \sqrt{3}

(2 \to a - 5 \to b) . (3 \to a + \to b) =

\to a

\to b

| \to a | = 3

| \to b | = 6

| \to a + \to b | = 7

(3 \to a - 2 \to b) . (2 \to a + 5 \to b - 4 \to a \times \to b)

\to p = 3 \to a - 5 \to b; \to q = 2 \to a + \to b; \to r = \to a + 4 \to b; \to s = - \to a + \to b

sin (\to p \land \to q) = 1

sin (\to r \land \to s) = 1

cos (\to a \land \to b)

\to a + 5 \to b = \to c

\to a - 7 \to b = 2 \to c

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