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

By triangle law, a⃗ + b⃗ + c⃗ = 0⃗ Taking cross product by a⃗, b⃗, c⃗ respectively, a⃗× (a⃗ + b⃗ + c⃗) = a⃗×0⃗ = 0⃗ ⇒a⃗×a⃗ + a⃗×b⃗ + a⃗×c⃗ = 0 ⇒a⃗×b⃗ = c⃗×a⃗ ...

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Byju's Answer

Standard XIII

Mathematics

Applications of Cross Product

If the vector...

Question

If the vectors $\to a, \to b$ and $\to c$ form the sides BC, CA and AB respectively of a $Δ A B C$ , 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

The correct option is B $\to a \times \to b = \to b \times \to c = \to c \times \to a$
By triangle law, $\to a + \to b + \to c = \to 0$

Taking cross product by $\to a, \to b, \to c$ respectively,
$\to a \times (\to a + \to b + \to c) = \to a \times \to 0 = \to 0 \Rightarrow \to a \times \to a + \to a \times \to b + \to a \times \to c = 0 \Rightarrow \to a \times \to b = \to c \times \to a [∵ \to a \times \to a = \to 0] Similarly, \to a \times \to b = \to b \times \to c ∴ \to a \times \to b = \to b \times \to c = \to c \times \to a$

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