If A-a-2 b-3 c- B-2 a-3 b-2 c- C-8 a-13b- Then A-B- and A-C- are collinearTrueFalse

The correct option is A TrueA⃗B⃗=O⃗B⃗ O⃗A⃗ =( 2a⃗+3b⃗+2c⃗) (a⃗ 2b⃗+3c⃗) = 3a⃗+5b⃗ c⃗ A⃗C⃗=O⃗C⃗ O⃗A⃗ =( 8a⃗+13b⃗) (a⃗ 2b⃗+3c⃗) = 9a⃗+15b⃗ 3c⃗ =3( 3a⃗+5 ...

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Byju's Answer

Standard XII

Mathematics

Test for Collinearity of Points

If A⃗=(a⃗-2 b...

Question

If $\to A = (\to a - 2 \to b + 3 \to c)$
$\to B = (- 2 \to a + 3 \to b + 2 \to c)$
$\to C = (- 8 \to a + 13 \to b)$
Then $\to A B$ and $\to A C$ are collinear

True

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False

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Solution

The correct option is A True
$\to A B = \to O B - \to O A = (- 2 \to a + 3 \to b + 2 \to c) - (\to a - 2 \to b + 3 \to c) = - 3 \to a + 5 \to b - \to c \to A C = \to O C - \to O A = (- 8 \to a + 13 \to b) - (\to a - 2 \to b + 3 \to c) = - 9 \to a + 15 \to b - 3 \to c = 3 (- 3 \to a + 5 \to b - \to c) = 3 \to A B \Rightarrow \to A C = 3 \to A B S o, \to A C i s p a r a l l e l t o \to A B But they have a common point A S o \to A C a n d \to A B a r e c o l l i n e a r$

Suggest Corrections

Similar questions

Q. If

\to A = (\to a - 2 \to b + 3 \to c)

\to B = (- 2 \to a + 3 \to b + 2 \to c)

\to C = (- 8 \to a + 13 \to b)

Then

\to A B

and

\to A C

are collinear

Q. If

\to a, \to b, \to c

are three non coplanar vectors,

\to p = \frac{\to b \times \to c}{[\to a \to b \to c]}

\to q = \frac{\to c \times \to a}{[\to a \to b \to c]}

\to r = \frac{\to a \times \to b}{[\to a \to b \to c]}

, then

(2 \to a + 3 \to b + 4 \to c) . \to p + (2 \to b + 3 \to c + 4 \to a) . \to q +

(2 \to c + 3 \to a + 4 \to b) . \to r =

Q. If

\to a, \to b, \to c

are unit vectors, then the maximum value of

| 2 \to a - 3 \to b |^{2} + | 2 \to b - 3 \to c |^{2} + | 2 \to c - 3 \to a |^{2}

Q. Four points given by position vectors

2 \to a + 3 \to b - \to c, \to a - 2 \to b + 3 \to c, 3 \to a + 4 \to b - 2 \to c a n d \to a - 6 \to b + 6 \to c

are coplanar, where

\to a, \to b a n d \to c

are non-coplanar vectors.

Q. If

\to a, \to b, \to c

are non coplanar and

[\to a \to b \to c] = \frac{4}{7}

, then

[2 \to a - \to b, 2 \to b - \to c, 2 \to c - \to a]

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If →A=(→a−2→b+3→c) →B=(−2→a+3→b+2→c) →C=(−8→a+13→b) Then →AB and →AC are collinear

If $\to A = (\to a - 2 \to b + 3 \to c)$
$\to B = (- 2 \to a + 3 \to b + 2 \to c)$
$\to C = (- 8 \to a + 13 \to b)$
Then $\to A B$ and $\to A C$ are collinear