Let -a-b-ck-b-c-ak- and -c-a-bk- be three coplanar vectors with a- b- c- and v-k- then v- is perpendicular to

The correct options are A #160;α B #160;β C #160;γ D All of these μα̅+λβ̅+kγ̅=0̅ [ a amp;b #160; amp;c; b #160; amp;c #160; a ...

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Byju's Answer

Standard XII

Mathematics

Area of Triangle with Coordinates of Vertices Given

Let α⃗=aî+b...

Question

Let $\to α = a^i + b^j + c^k, \to β = b^i + c^j + a^k$ and $\to γ = c^i + a^j + b^k$ be three coplanar vectors with $a \neq b \neq c$ , and $\to v =^i +^j +^k$ , then $\to v$ is perpendicular to

\to α

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\to β

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\to γ

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All of these

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Solution

The correct options are
A $\to α$
B $\to β$
C $\to γ$
D All of these
$μ ¯ α + λ ¯ β + k ¯ γ = ¯ 0$
$⎡ ⎢ ⎣ \begin{matrix} a & b & c b & c & a c & a & b \end{matrix} ⎤ ⎥ ⎦ ⎡ ⎢ ⎣ \begin{matrix} μ λ k \end{matrix} ⎤ ⎥ ⎦ = \to 0$
$R_{1} \to R_{1} + R_{2} + R_{3}$
$(a + b + c) ⎡ ⎢ ⎣ \begin{matrix} 1 & 1 & 1 b & c & a c & a & b \end{matrix} ⎤ ⎥ ⎦ ⎡ ⎢ ⎣ \begin{matrix} μ λ k \end{matrix} ⎤ ⎥ ⎦ = \to 0$
$a + b + c ⎡ ⎢ ⎣ \begin{matrix} 1 & 0 & 0 b & c - b & a - b c & a - c & b - c \end{matrix} ⎤ ⎥ ⎦ ⎡ ⎢ ⎣ \begin{matrix} μ λ k \end{matrix} ⎤ ⎥ ⎦ = ¯ 0$
which mean $a + b + c = 0$ as $a \neq b \neq c$
$\to α . \to V = \to β . \to V = \to γ . \to V = a + b + c = 0$

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Let →α=a^i+b^j+c^k,→β=b^i+c^j+a^k and →γ=c^i+a^j+b^k be three coplanar vectors with a≠b≠c, and →v=^i+^j+^k, then →v is perpendicular to

Let $\to α = a^i + b^j + c^k, \to β = b^i + c^j + a^k$ and $\to γ = c^i + a^j + b^k$ be three coplanar vectors with $a \neq b \neq c$ , and $\to v =^i +^j +^k$ , then $\to v$ is perpendicular to