You visited us 3 times! Enjoying our articles? Unlock Full Access!

Test for Collinearity of Vectors

Let a , b...

Question

Let $a$ , $b$ and $c$ are three vectors of which every pair is non-collinear. If $a + c$ and $b + c$ are collinear with $b$ and $a$ respectively, then $a + b + c$ is equal to:

0

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

2

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

- 1

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 $0$
Given $a + c$ is collinear with $b$ , so we get $a + c = λ b$
$\Rightarrow a + b + c = (1 + λ) b$
Given $b + c$ is collinear with $a$ , so we get $b + c = β a$
$\Rightarrow a + b + c = (1 + β) a$
So by equating above two , we get $(1 + λ) b - (1 + β) a = 0$
Given that $a, b$ are not collinear
So we get $λ + 1 = 0$ and $β + 1 = 0$
$\Rightarrow λ = β = - 1$
Therefore $a + b + c = (1 + λ) b = (1 - 1) a = 0$
So the correct option is $A$

Suggest Corrections

Similar questions

Q. If

\vec{a}, \vec{b}, \vec{c}

are three non-zero vectors, no two of which are collinear and the vector

\vec{a} + \vec{b}

is collinear with

\vec{c}, \vec{b} + \vec{c}

is collinear with

\vec{a},

then

\vec{a} + \vec{b} + \vec{c} =

(a)

\vec{a}

(b)

\vec{b}

(c)

\vec{c}

(d) none of these

Q. Let a,b and c be three nonzero vectors, no two of which are collinear. If the vector a+2b is collinear with c, and b+3c is collinear with a, then a+2b+6c =

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

Q. Let a, b and c be three non - zero vectors which are pairwise non- collinear. If a + 3b is collinear with c and b + 2c is collinear with a, then a + 3b + 6c is equal to

Q. Let

\to a, \to b, \to c

are three non zero vectors such that any two of them are non-collinear. If

\to a + \to b

is collinear with

\to c

and

\to b + \to c

is collinear with

\to a

, then the value of

\to a + \to b + \to c

equals

Join BYJU'S Learning Program

Let a , b and c are three vectors of which every pair is non-collinear. If a+c and b+c are collinear with b and a respectively, then a+b+c is equal to:

Let $a$ , $b$ and $c$ are three vectors of which every pair is non-collinear. If $a + c$ and $b + c$ are collinear with $b$ and $a$ respectively, then $a + b + c$ is equal to: