If a -k- b -2 -k- and c - x - y k- are linearly dependent and - c -3 then x - y isA- -1-1B- 2-3C- 3-1

The correct option is A ( 1, 1)Given that the three vectors are linearly dependent so c⃗=la⃗+mb⃗ ⇒ l+2m=1(Comparing the î components) l m =x (Comparing the ĵ c ...

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

Byju's Answer

Standard XII

Mathematics

Linear Dependence and Independence of Vectors

If a =î+ĵ+k̂,...

Question

If $\to a =^i +^j +^k, \to b = 2^i -^j +^k$ and $\to c =^i + x^j + y^k$ , are linearly dependent and $| \to c | = \sqrt{3}$ then (x,y) is

(-1, -1)

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

(2,3)

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

(3,1)

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

Open in App

Solution

The correct option is A (-1, -1)
Given that the three vectors are linearly dependent so
$\to c = l \to a + m \to b$
$\Rightarrow l + 2 m = 1$ (Comparing the $^i$ components)
$l - m = x$ (Comparing the $^j$ components)
$\Rightarrow x - 3 y = 2$
I +m =y (Comparing the $^k$ components)
Also, $x^{2} + y^{2} + 1 = 3$
$10 y^{2} + 12 y + 2 = 0$
$\Rightarrow y = - 1, - \frac{1}{5}$
$x = - 1, \frac{7}{5}$

Suggest Corrections

Similar questions

Q. If

\to a =^i +^j +^k, \to b = 2^i -^j +^k

and

\to c =^i + x^j + y^k

, are linearly dependent and

| \to c | = \sqrt{3}

then

(x, y)

Q. If

\to a =^i +^j +^k, \to b = 2^i -^j +^k

and

\to c =^i + x^j + y^k

, are linearly dependent and

| \to c | = \sqrt{3}

then

(x, y)

Q. If

\to a =^i +^j +^k, \to b = 2^i +^j +^k

and

\to c =^i + x^j + y^k

, are linearly dependent and

| \to c | = \sqrt{3}

then (x,y) is

Q. Let

\to a =^i -^k, \to b = x^i +^j + (1 - x)^k

and

\to c = y^i + x^j + (1 - x - y)^k

, then

[\to a \to b \to c]

depends on

Q. Let

\to a =^i -^k, \to b = x^i +^j + (1 - x)^k, \to c = y^i + x^j + (1 + x - y)^k

. then

[\to a \to b \to c]

depends on

Join BYJU'S Learning Program

If →a=^i+^j+^k,→b=2^i−^j+^k and →c=^i+x^j+y^k, are linearly dependent and |→c|=√3 then (x,y) is

The correct option is A (-1, -1)Given that the three vectors are linearly dependent so →c=l→a+m→b ⇒l+2m=1(Comparing the ^i components) l−m=x (Comparing the ^j components) ⇒x−3y=2 I +m =y (Comparing the ^k components) Also, x2+y2+1=3 10y2+12y+2=0 ⇒y=−1,−15 x=−1,75

If $\to a =^i +^j +^k, \to b = 2^i -^j +^k$ and $\to c =^i + x^j + y^k$ , are linearly dependent and $| \to c | = \sqrt{3}$ then (x,y) is