If a -k- b -2 -k- and c - x - y k- are linearly dependent and - c -3 then x - y isA- 1-1 B- 1-5- 7-5- -2-0D- -7-5- 3-5

The correct option is A (1, 1)Given that the three vectors are linearly dependent so c⃗=la⃗+mb⃗ ⇒ l+2m=1 l m =x ⇒ x =3y 2 I +m =y Also, x^2+y^2+1=3 10y^2 12y+ ...

You visited us 2 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard IX

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, 0)

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

(\frac{1}{5}, \frac{7}{5})

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

(- \frac{7}{5}, \frac{3}{5})

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
$\to c = l \to a + m \to b$
$\Rightarrow l + 2 m = 1$
$l - m = x$
$\Rightarrow x = 3 y - 2$
I +m =y
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 l−m=x ⇒x=3y−2 I +m =y 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

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