If A-B- and C- are vectors such that -B- - -C- prove that - A- - B- - A- - C- - B-C- B- - C- - 0-

[ we have( A⃗ + B⃗) ×( A⃗ + C⃗) = A⃗×C⃗ + B⃗×A⃗ + B⃗×C⃗; #160;⇒[ ( A⃗ + B⃗) ×( A⃗ + C⃗)] ×( B⃗×C⃗) = [ ...

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Condition for Coplanarity of Four Points

If A⃗,B⃗ an...

Question

If $\to A, \to B$ and $\to C$ are vectors such that $| \to B | = | \to C |$ , prove that
$[(\to A + \to B) \times (\to A + \to C)] \times (\to B \times \to C) . (\to B + \to C) = 0$ .

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Solution

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Similar questions

\to A, \to B

\to C

(\to A + \to B + \to C)

[(\to A + \to B) \times (\to A + \to C)]

\to a, \to b

\to c

\to p, \to q

\to r

\to p = \frac{\to b \times \to c}{[\to a \to b \to c]}, \to q = \frac{\to c \times \to a}{[\to a \to b \to c]}, \to r = \frac{\to a \times \to b}{[\to a \to b \to c]}

(\to a + \to b) \cdot \to p + (\to b + \to c) \cdot \to q + (\to c + \to a) \cdot \to r =

\to a + 2 \to b + 3 \to c = 0

\to a \times \to b + \to b \times \to c + \to c \times \to a

λ (\to b \times \to c)

λ

\to a = 2^i +^j - 2^k

\to b =^i +^j

\to c

\to a . \to c = | \to c |

| \to c - \to a | = 2 \sqrt{2}

(\to a \times \to b)

\to c

30^{0}

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

\to a, \to b

| \to a | = 1, ∣ ∣ \to b ∣ ∣ = 4, \to a . \to b = 2

\to c = 2 (\to a \times \to b) - 3 \to b

\to b

\to c

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