If a- b- c- are three unit vectors- each is inclined at an angle -3 with other- find - a- b- c-

Given the unit vector are.........a,b,c #160; #160; #160; #160; | a | = | b | = | c | = 1 According to question.......Angle π3 or #160; an ...

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Applications of Dot Product

If a⃗, b⃗, ...

Question

If $\to a, \to b, \to c$ are three unit vectors, each is inclined at an angle $\frac{π}{3}$ with other, find [ $\to a, \to b, \to c$ ].

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Solution

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\to a, \to b, \to c

\frac{π}{3}

[\to a \to b \to c]

\to a, \to b, \to c

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

(\to a, \to b) = \frac{π}{3}

∣ ∣ \to a \times \to b ∣ ∣ + ∣ ∣ \to b \times \to c ∣ ∣ + | \to c \times \to a | =

\to a, \to b, \to c

\to c

α

\to a

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\to b

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

\to a, \to b, \to c

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\frac{π}{6}, \frac{π}{3}

\frac{π}{4}

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

\to a, \to b, \to c

\frac{π}{3}

| \to a | = 1, | \to b | = 2, | \to c | = 3

2 \to a + 3 \to b - 5 \to c

4 \to a - 6 \to b + 10 \to c

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