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

Byju's Answer

Standard XII

Mathematics

Test for Collinearity of Vectors

Let a, b an...

Question

Let $a, b$ and $c$ be three non-zero vectors, no two of which are collinear. If the vector $a + 2 b$ is collinear with $c,$ and $b + 3 c$ is collinear with $a,$ then $a + 2 b + 6 c$ is equal to
$(λ$ being some non-zero scalar) then $a + 2 b + 6 c =$

λ a

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

λ b

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

λ c

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

0

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

Open in App

Solution

The correct option is B $0$
Let $a + 2 b = x c$ and $b + 3 c = y a$ .
Then $a + 2 b + 6 c = (x + 6) c$
and also, $a + 2 b + 6 c = (1 + 2 y) a,$
So $(x + 6) c = (1 + 2 y) a .$
Since $a, b$ and $c$ are non-zero and non-collinear,
we have $x + 6 = 0$
and $1 + 2 y = 0,$ i.e. $x = - 6$ and $y = - 1 / 2,$
In either case, we have $a + 2 b + 6 c = 0$

Suggest Corrections

Similar questions

Q. Let

a, b, c

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

a + 2 b

is collinear with

c

and

b + 3 c

is collinear with

a

(

λ

being some non-zero scalar), then

a + 2 b + 6 c

equals to

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

a

b

and

c

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

a + 2 b

is collinear with

c

and

b + 3 c

is collinear with

a

.then

a + 2 b + 6 c

is equal to :

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

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

Join BYJU'S Learning Program

Let a,b and c be three non-zero 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 is equal to(λ being some non-zero scalar) then a+2b+6c=

The correct option is B 0Let a+2b=xc and b+3c=ya. Then a+2b+6c=(x+6)c and also, a+2b+6c=(1+2y)a, So (x+6)c=(1+2y)a. Since a,b and c are non-zero and non-collinear, we have x+6=0 and 1+2y=0, i.e. x=−6 and y=−1/2, In either case, we have a+2b+6c=0

Let $a, b$ and $c$ be three non-zero vectors, no two of which are collinear. If the vector $a + 2 b$ is collinear with $c,$ and $b + 3 c$ is collinear with $a,$ then $a + 2 b + 6 c$ is equal to
$(λ$ being some non-zero scalar) then $a + 2 b + 6 c =$