If a-b-c- are three non-zero vectors such that a-b-c- and b-c-a- - then choose the incorrect options

The correct options are B | b⃗ |= | c⃗ | C a⃗ is a unit vector D c⃗ is a unit vector a⃗×b⃗=c⃗⇒ nbsp; a⃗.c⃗=0=b⃗.c⃗ b⃗×c⃗=a⃗⇒ nbsp ...

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Byju's Answer

Standard XII

Physics

Unit Vectors

If a⃗,b⃗,c⃗...

Question

If $\to a, \to b, \to c$ are three non-zero vectors such that $\to a \times \to b = \to c$ and $\to b \times \to c = \to a$ , then choose the incorrect option(s)

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

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∣ ∣ \to b ∣ ∣ = | \to c |

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\to a

is a unit vector

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\to c

is a unit vector

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Solution

The correct options are
B $∣ ∣ \to b ∣ ∣ = | \to c |$
C $\to a$ is a unit vector
D $\to c$ is a unit vector
$\to a \times \to b = \to c \Rightarrow \to a . \to c = 0 = \to b . \to c$
$\to b \times \to c = \to a \Rightarrow \to a . \to b = 0 = \to a . \to c$
$\Rightarrow \to a, \to b, \to c$ are mutually pependicular vectors.
$∴ \to a \times \to b = \to c \Rightarrow | \to a | ∣ ∣ \to b ∣ ∣ = | \to c |$
$\to b \times \to c = \to a \Rightarrow ∣ ∣ \to b ∣ ∣ | \to c | = | \to a |$
$∴ {∣ ∣ \to b ∣ ∣}^{2} | \to c | = | \to c | \Rightarrow ∣ ∣ \to b ∣ ∣ = 1$
$∴ | \to a | = | \to c |$
Hence, options B , C and D are incorrect.

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Similar questions

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If →a,→b,→c are three non-zero vectors such that →a×→b=→c and →b×→c=→a , then choose the incorrect option(s)

If $\to a, \to b, \to c$ are three non-zero vectors such that $\to a \times \to b = \to c$ and $\to b \times \to c = \to a$ , then choose the incorrect option(s)