A-2-k- lies in plane of vactor b- and c-k- and bisects - between b- c- possible value of - and -

The correct option is A 1, 1 → As a⃗ lies in plane #160;containing b⃗ and c⃗, ⇒ #160; a⃗ is perpendicular to #160; b ...

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Byju's Answer

Standard XII

Mathematics

Family of Planes Passing through the Intersection of Two Planes

a⃗=αî+2ĵ+βk̂ ...

Question

$\to a = α^i + 2^j + β^k$ lies in plane of vactor $\to b =^i +^j$ and $\to c =^j +^k$ and bisects $<$ between $\to b$ & $\to c$ possible value of $α$ and $β$ ?

1, 1

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Solution

The correct option is A $1, 1$
$\to$ As $\to a$ lies in plane
containing $\to b$ and $\to c,$
$\Rightarrow \to a$ is perpendicular to
$\to b \times \to c = (^l +^j) \times (^j +^k) =^j +^k -^l$
$\Rightarrow \to a (^l -^j +^k) = 0$
$\Rightarrow α - 2 + β = 0 \Rightarrow α + β = 2$
and angle between $\to a$ and $\to b$
is equal to that between $\to a$ and $\to b$
$\Rightarrow \frac{\to a - \to b}{| \to a | ∣ ∣ \to b ∣ ∣} = \frac{\to a - \to c}{| \to a | | \to c |} \Rightarrow \frac{α + 2}{\sqrt{2}} = \frac{2 + β}{\sqrt{2}}$
$\Rightarrow α - β = 0 \Rightarrow α = β \Rightarrow α = β = 1$
$\Rightarrow (A)$

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→a=α^i+2^j+β^k lies in plane of vactor →b=^i+^j and →c=^j+^k and bisects < between →b & →c possible value of α and β?

$\to a = α^i + 2^j + β^k$ lies in plane of vactor $\to b =^i +^j$ and $\to c =^j +^k$ and bisects $<$ between $\to b$ & $\to c$ possible value of $α$ and $β$ ?