Let a-k- b-2k- and c-x-x-2-k-If the vector c lies in the plane of a and b-then x-

The correct option is C 2 a,b,c are coplanar ∴[abc]=(a×b).c=0 ⇒| 1 amp;1 amp;1 nbsp; 1 amp; 1 amp; 2 x amp; ( ...

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Byju's Answer

Standard XII

Mathematics

Equation of a Plane Passing through Three Points

Let a=î+ĵ+k...

Question

Let $\to a =^i +^j +^k, \to b =^i -^j + 2^k$ and $\to c = x^i + (x - 2)^j -^k$
If the vector $\to c$ lies in the plane of $\to a$ and $\to b$ ,then $x =$

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Solution

The correct option is C $- 2$
$\to a, \to b, \to c$ are coplanar
$∴ [\to a \to b \to c] = (\to a \times \to b) . \to c = 0$
$\Rightarrow ∣ ∣ ∣ ∣ \begin{matrix} 1 & 1 & 1 1 & - 1 & 2 x & (x - 2) & - 1 \end{matrix} ∣ ∣ ∣ ∣$
$\Rightarrow 1 - 2 (x - 2) - (- 1 - 2 x) + x - 2 + x = 0$
$\Rightarrow 2 x + 4 = 0$ on simplification
$∴ x = - 2$

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Similar questions

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Let →a=^i+^j+^k,→b=^i−^j+2^k and →c=x^i+(x−2)^j−^kIf the vector →c lies in the plane of →a and →b,then x=

The correct option is C −2→a,→b,→c are coplanar∴[→a→b→c]=(→a×→b).→c=0⇒∣∣ ∣∣1111−12x(x−2)−1∣∣ ∣∣⇒1−2(x−2)−(−1−2x)+x−2+x=0⇒2x+4=0 on simplification∴x=−2

Let $\to a =^i +^j +^k, \to b =^i -^j + 2^k$ and $\to c = x^i + (x - 2)^j -^k$
If the vector $\to c$ lies in the plane of $\to a$ and $\to b$ ,then $x =$