If a-b-c are three non-zero vectors and a-b- a-c-b-c- then

The correct option is C a b is parallel to c We get #160; (a⃗ b⃗)×c⃗=0 So #160; #160; (a⃗ b⃗)∥c⃗ ...

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Byju's Answer

Standard VII

Mathematics

Intersecting Lines

If a,b,c ar...

Question

If $¯ ¯ ¯ a, ¯ ¯ b, ¯ ¯ c$ are three non-zero vectors and $¯ ¯ ¯ a \neq ¯ ¯ b$ , $¯ ¯ ¯ a \times ¯ ¯ c = ¯ ¯ b \times ¯ ¯ c$ , then

¯ ¯ ¯ a - ¯ ¯ b

is parallel to

¯ ¯ c

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¯ ¯ ¯ a - ¯ ¯ b

is perpendicular to

¯ ¯ c

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¯ ¯ ¯ a + ¯ ¯ b

is parallel to

¯ ¯ c

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¯ ¯ ¯ a + ¯ ¯ b

is perpendicular to

¯ ¯ c

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Solution

The correct option is C $¯ ¯ ¯ a - ¯ ¯ b$ is parallel to $¯ ¯ c$
We get
$(\to a - \to b) \times \to c = 0$
So $(\to a - \to b) ∥ \to c$

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If ¯¯¯a,¯¯b,¯¯c are three non-zero vectors and ¯¯¯a≠¯¯b, ¯¯¯a×¯¯c=¯¯b×¯¯c, then

The correct option is C ¯¯¯a−¯¯b is parallel to ¯¯cWe get (→a−→b)×→c=0So (→a−→b)∥→c

If $¯ ¯ ¯ a, ¯ ¯ b, ¯ ¯ c$ are three non-zero vectors and $¯ ¯ ¯ a \neq ¯ ¯ b$ , $¯ ¯ ¯ a \times ¯ ¯ c = ¯ ¯ b \times ¯ ¯ c$ , then

The correct option is C $¯ ¯ ¯ a - ¯ ¯ b$ is parallel to $¯ ¯ c$
We get
$(\to a - \to b) \times \to c = 0$
So $(\to a - \to b) ∥ \to c$