If a-5b-c- and a-7b-2c- then

The correct option is A a⃗ and c⃗ are like but b⃗ and c⃗ are unlike vectorsGiven a⃗+5b⃗=c⃗ and a⃗ 7b⃗=2c⃗ Eliminating b ...

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Byju's Answer

Standard XII

Mathematics

Like and Unlike Vectors

If a⃗+5b⃗=c...

Question

If $\to a + 5 \to b = \to c$ and $\to a - 7 \to b = 2 \to c$ then

\to a

and

\to c

are like but

\to b

and

\to c

are unlike vectors

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\to a

and

\to b

unlike vectors and so also

\to a

and

\to c

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\to b

and

\to c

are like but

\to a

and

\to b

are unlike vectors

No worries! We‘ve got your back. Try BYJU‘S free classes today!

\to a

and

\to c

are unlike vectors and so also

\to b

and

\to c

No worries! We‘ve got your back. Try BYJU‘S free classes today!

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Solution

The correct option is A $\to a$ and $\to c$ are like but $\to b$ and $\to c$ are unlike vectors
Given $\to a + 5 \to b = \to c$ and $\to a - 7 \to b = 2 \to c$
Eliminating $\to b$ gives
$\frac{\to c - \to a}{5} = \frac{\to a - 2 \to c}{7}$
$\Rightarrow 7 \to c - 7 \to a = 5 \to a - 10 \to c$
$\Rightarrow 12 \to a = 17 \to c$ -----(1)
Eliminating $\to a$ gives
$\to c - 5 \to b = 2 \to c + 7 \to b$
$\to c = - 12 \to b$ -----(2)
$∴$ From (1) and (2)
$\to a$ and $\to c$ are like but $\to b$ and $\to c$ are unlike vectors.
Hence, option A is correct.

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If →a+5→b=→c and →a−7→b=2→c then

If $\to a + 5 \to b = \to c$ and $\to a - 7 \to b = 2 \to c$ then