Show that -a-b-b-a- is perpendicular to -a-b-b-a- for any two nonzero vectors a- and b- -

(|a⃗|b⃗+|b⃗|a⃗)· (|a⃗|b⃗ |b⃗|a⃗) =|#10; a|^2b⃗·b⃗ |a⃗||b⃗|b⃗·#10;a+|b⃗||a⃗|a⃗·b⃗ |b⃗|^2a⃗· #10; a⃗ =|a⃗|^2|b⃗|^2 |b⃗|^2|a⃗|^2=0 Hence, |a⃗ ...

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Sum of Infinite Terms of a GP

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Question

Show that $| \to a | \to b + | \to b | \to a$ is perpendicular to $| \to a | \to b - | \to b | \to a$ , for any two nonzero vectors $\to a$ and $\to b$ .

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| \to a | \to b + | \to b | \to a

| \to a | \to b - | \to b | \to a

\to a

\to b

| \to b | \to a + | \to a | \to b

| \to b | \to a - | \to a | \to b

^a

^b

| \to a + \to b | \leq | \to a | + | \to b |

| \to a - \to b | \leq | \to a | + | \to b |

\to a, \to b, \to c

\to a \times (\to b + \to c) + \to b \times (\to c + \to a) + \to c \times (\to a + \to b)

| \to b | \to a + | \to a | \to b a n d | \to b | \to a - | \to a | \to b

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