Let a-b-c- be three non-zero vectors such that c- is a unit vectors perpendicular is both a- and b- If the angle between a- and b- is -6- prove that - a- b- c- -2-14-a-2-b-2-

Since, c⃗ =λ( a⃗×b⃗ #160; ) #160; | c⃗ #160; | =1 Now, #160; [ a⃗ b⃗ c⃗ #160; ] ^ 2 =| c⃗ .( a⃗×b⃗ #160; ) #160; | ^ 2 =[ | ...

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Addition of Vectors

Let a⃗,b⃗,c...

Question

Let $\to a, \to b, \to c$ be three non-zero vectors such that $\to c$ is a unit vectors perpendicular is both $\to a$ and $\to b$ . If the angle between $\to a$ and $\to b$ is $\frac{π}{6}$ , prove that $[\to a \to b \to c]^{2} = \frac{1}{4} | \to a |^{2} | \to b |^{2}$ .

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\to a, \to b, \to c

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\to a \times (\to b \times \to c) = \frac{(\to b + \to c)}{\sqrt{2}},

\to a

\to b

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\to a \times (\to b \times \to c) = \frac{\to b + \to c}{\sqrt{2}}

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α

β

\to a, \to b, \to c

\to a + \to b + \to c = \to 0,

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| \to a | = \sqrt{3}, | \to b | = 5, \to b . \to c = 10

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