If a-b-c- and b-c-a-then

The correct option is A a⃗, b⃗,c⃗ are orthogonal in pairs and |a⃗|=|b⃗| and |c⃗|=1.c⃗=a⃗×b⃗⇒ amp;c⃗⊥a⃗ amp; and c⃗⊥b⃗ a⃗=b⃗×c⃗⇒ amp;a⃗⊥b⃗ amp; and a⃗ ...

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Byju's Answer

Standard IX

Mathematics

Vector Triple Product

If a⃗×b⃗=c⃗ a...

Question

If $\to a \times \to b = \to c$ and $\to b \times \to c = \to a$ ,then

\to a, \to b, \to c

are orthogonal in pairs and

| \to a | = | \to b |

and

| \to c | = 1

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\to a, \to b, \to c

are not orthogonal to each other

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\to a, \to b, \to c

are orthogonal in pairs but

| \to a | \neq | \to c |

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\to a, \to b, \to c

are orthogonal but

| \to b | \neq 1

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Solution

The correct option is A $\to a, \to b, \to c$ are orthogonal in pairs and $| \to a | = | \to b |$ and $| \to c | = 1$
$\begin{matrix} \to c = \to a \times \to b \Rightarrow & \to c ⊥ \to a & a n d \to c ⊥ \to b \to a = \to b \times \to c \Rightarrow & \to a ⊥ \to b & a n d \to a ⊥ \to c \end{matrix}} \Rightarrow \to a ⊥ \to b ⊥ \to c$
Now, $\to a \times \to b = \to c$
$\Rightarrow (\to b \times \to c) \times \to b = \to c [s i n c e \to a = \to b \times \to c] \Rightarrow (\to b . \to b) \to c - (\to b . \to c) \to b = \to c \Rightarrow | \to b |^{2} \to c = \to c [\to b ⊥ \to c, ∴ \to b . \to c = 0] \Rightarrow | \to b | = 1$
Also, $\to c = \to a \times \to b$
$\Rightarrow | \to c | = | \to a \times \to b | \Rightarrow | \to c | = | \to a | \times | \to b | s i n \frac{π}{2} \Rightarrow | \to c | = | \to a | (∴ | \to b | = 1)$

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If →a×→b=→c and →b×→c=→a,then

If $\to a \times \to b = \to c$ and $\to b \times \to c = \to a$ ,then