If the vectors a-b-c- form the sides BC-CA and AB respectively of a triangle ABC- then-

The correct option is B a⃗×b⃗=b⃗×c⃗=c⃗×a⃗ #10; #10; #10; #10; #10; #10; #10; #10;Area of triangle =1/2[ a⃗×b⃗ ]=1/2[ b⃗×c⃗ ]=1/2[ c⃗ ...

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Condition for Coplanarity of Four Points

If the vector...

Question

If the vectors $\to a, \to b, \to c$ form the sides $B C, C A a n d A B$ respectively of a triangle $A B C$ , then:

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

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\to a \times \to b = \to b \times \to c = \to c \times \to a

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\to a . \to b = \to b . \to c = \to c . \to a

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

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Solution

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[\to a \to b \to c] = 2

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

[\begin{matrix} \to a & \to b & \to c \end{matrix}] = 1

\frac{\to a . \to b \times \to c}{\to c \times \to a . \to b} + \frac{\to b . \to c \times \to a}{\to a \times \to b . \to c} + \frac{\to c . \to a \times \to b}{\to b \times \to c . \to a}

\to a, \to b, \to c

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

\to a . \to b + \to b . \to c + \to c . \to a

\to a, \to b, \to c

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

μ = \to a . \to b + \to b . \to c + \to c . \to a

| \to a | = 1; ∣ ∣ \to b ∣ ∣ = 4; | \to c | = 2

| \to a |, ∣ ∣ \to b ∣ ∣

| \to c |

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

λ = \to a . \to b + \to b . \to c + \to c . \to a

| \to a | = 1, ∣ ∣ \to b ∣ ∣ = 4 a n d | \to c | = 2

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