The vector a-2-k- lies in the plane of vectors b- and c-k- and bisect the angle between b- and c- then which one of the following gives possible values of - and - -

The correct option is B β =α =1 As vector a̅ lies in the plane of b̅ amp; #160; c̅ #160; ∴ [a̅b̅c̅]=0 ⇒ #160;α amp;2 ...

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Standard XII

Physics

Multiplication with Vectors

The vector ...

Question

The vector $\to a = α^i + 2^j + β^k$ lies in the plane of vectors $\to b =^i +^j,$ and $\to c =^j +^k$ and bisect the angle between $\to b$ and $\to c$ then which one of the following gives possible values of $α$ and $β$ ?

α = 1, β = 2

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α = 2, β = 1

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β = α = 1

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α = β = 2

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Solution

The correct option is B $β = α = 1$
As vector $¯ a$ lies in the plane of $¯ b$ & $¯ c$

$∴ [¯ a ¯ b ¯ c] = 0$ $\Rightarrow ∣ ∣ ∣ ∣ \begin{matrix} α & 2 & β 1 & 1 & 0 0 & 1 & 1 \end{matrix} ∣ ∣ ∣ ∣ = 0 \Rightarrow α + β = 0 . . . . (1)$

Again $¯ a$ bisect the angle between $¯ b$ and $¯ c$
$∴ ¯ a \cdot ¯ b = ¯ a \cdot ¯ c$
$\Rightarrow α + 2 = β + 2 \Rightarrow α = β . . . . (2)$

Solving $(1)$ & $(2)$ we get $α = 1, β = 1$

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The vector →a=α^i+2^j+β^k lies in the plane of vectors →b=^i+^j, and →c=^j+^k and bisect the angle between →b and →c then which one of the following gives possible values of α and β ?

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