If a- -b- -c- are three non-zero vectors- no two of which are collinear and the vector a- -b- is collinear with c- b- -c- is collinear with a- then a- -b- -c- is equal to -

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Question

If $\to a, \to b, \to c$ are three non-zero vectors, no two of which are collinear and the vector $\to a + \to b$ is collinear with $\to c, \to b + \to c$ is collinear with $\to a,$ then $\to a + \to b + \to c$ is equal to -

\to a

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\to b

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\to c

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n o n e o f t h e s e

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Solution

The correct option is C $n o n e o f t h e s e$
$¯ a + ¯ b = K_{1} ¯ c$

$¯ b + ¯ c = K_{2} ¯ a$

$¯ a - ¯ c = K_{1} c - K_{2} ¯ a$

$(k_{2} + 1) ¯ a - ¯ c (1 + k_{1})$ =0

$k_{2} = - 1$ and $k_{1} = - 1$

$¯ a + ¯ b + ¯ c = 0$

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If →a,→b,→c are three non-zero vectors, no two of which are collinear and the vector →a+→b is collinear with →c,→b+→c is collinear with →a, then →a+→b+→c is equal to -

The correct option is C none of these¯a+¯b=K1¯c¯b+¯c=K2¯a¯a−¯c=K1c−K2¯a(k2+1)¯a−¯c(1+k1)=0k2=−1 and k1=−1¯a+¯b+¯c=0

If $\to a, \to b, \to c$ are three non-zero vectors, no two of which are collinear and the vector $\to a + \to b$ is collinear with $\to c, \to b + \to c$ is collinear with $\to a,$ then $\to a + \to b + \to c$ is equal to -

The correct option is C $n o n e o f t h e s e$
$¯ a + ¯ b = K_{1} ¯ c$

$¯ b + ¯ c = K_{2} ¯ a$

$¯ a - ¯ c = K_{1} c - K_{2} ¯ a$

$(k_{2} + 1) ¯ a - ¯ c (1 + k_{1})$ =0

$k_{2} = - 1$ and $k_{1} = - 1$

$¯ a + ¯ b + ¯ c = 0$