If a- b- c- are three non-zero vectors- no two of which are collinear- a-b- is collinear with c- and b-3 c- is collinear with a- then -a-2 b-6 c- will be equal to

The correct option is D zero a⃗+2b⃗=λc⃗...(i) b⃗+3c⃗=μa⃗,......(ii) where no two of a⃗, b⃗ and c⃗ are collinear vectors Eliminating b⃗ from above relations, ⇒ ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard IX

Mathematics

Collinear Vectors

If a⃗, b⃗, c⃗...

Question

If $\to a, \to b, \to c$ are three non-zero vectors, no two of which are collinear, $\to a + \to b$ is collinear with $\to c$ and $\to b + 3 \to c$ is collinear with $\to a$ , then $| \to a + 2 \to b + 6 \to c |$ will be equal to

zero

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

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

None of these

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

Open in App

Solution

The correct option is A
zero

$\to a + 2 \to b = λ \to c . . . (i) \to b + 3 \to c = μ \to a, . . . . . . (i i)$
where no two of $\to a, \to b a n d \to c$ are collinear vectors
Eliminating $\to b$ from above relations,
$\Rightarrow \to a - 6 \to c = λ \to c - 2 μ \to a \Rightarrow \to a (1 + 2 μ) = (λ + 6) \to c$
Since $\to a, \to b$ are non-collinear and non-zero,
$1 + 2 μ = 0, λ + 6 = 0 \Rightarrow μ = - \frac{1}{2}, λ = - 6$

$\to a + 2 \to b = - 6 \to c \Rightarrow \to a + 2 \to b + 6 \to c = \to 0$

Suggest Corrections

Similar questions

Let $\to a, \to b$ and $\to c$ be three non -zero vectors such that they are mutually non collinear. If the vector $\to a + 2 \to b$ is collinear with $\to c$ and $\to b + 3 \to c$ is collinear with $\to a$ then $\to a + 2 \to b + 6 \to c$ equals

Q. Let

\to a, \to b

and

\to c

be three non-zero vectors such that no two of these are collinear. If the vector

\to a + 2 \to b

is collinear with

\to c

and

\to b + 3 \to c

is collinear with

\to a (λ

being some non-zero scalar), then

\to a + 2 \to b + 6 \to c

equals

Q. Let

\to a, \to b

and

\to c

be three non-zero vectors such that no two of these are collinear. If the vector

\to a + 2 \to b

is collinear with

\to c

and

\to b + 3 \to c

is collinear with

\to a

(

λ

being some non-zero scalar) then

\to a + 2 \to b + 6 \to c

equals

If $\to a, \to b, \to c$ are three non-zero vectors, no two of which are collinear, $\to a + \to b$ is collinear with $\to c$ and $\to b + 3 \to c$ is collinear with $\to a$ , then $| \to a + 2 \to b + 6 \to c |$ will be equal to