If a-k- b-2-k- and c-x-yk- are linearly dependent and -c-3 then x-y is

Given that the three vectors are linearly dependent so c=la+mb ⇒ l+2m=1 l m =x ⇒ x =3y 2 l +m =y Also, x^2+y^2+1=3 10y^2 12y+2=0 ⇒ y=1, 1/5 x=1, 7/5 nbsp; ...

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Standard XIII

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)

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(- 2, 0)

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

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

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Solution

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

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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 l+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