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

Consider the problem [ ( | a⃗ #160; | b⃗ +| b⃗ #160; | a⃗ #160; ) ·( | a⃗ #160; | b⃗ | b⃗ #1 ...

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Applications of Dot Product

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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

^a

^b

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

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

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

| \to b | \to a - | \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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