If x is parallel to y and z where x - 2-k- y - - - k- and z - 5- - - then - is equal to

Given x is parallel to y and z ∴ x.(y× z) = nbsp; 0 ⇒ [x y z] = 0 ⇒ 2 amp; 1 amp; α α nbsp; amp; 0 amp; 1 5 amp; 1 amp; 0 =0 ⇒α=±√(7 ...

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Standard XII

Mathematics

Scalar Triple Product

If x is paral...

Question

If $x$ is parallel to $y$ and $z$ where $x = 2^i +^j + α^k, y = α^i +^k$ and $z = 5^i -^j,$ then $α$ is equal to

\pm \sqrt{5}

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\pm \sqrt{6}

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\pm \sqrt{7}

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None of these

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Solution

The correct option is C $\pm \sqrt{7}$
Given $x$ is parallel to $y$ and $z$
$∴ x . (y \times z) = 0 \Rightarrow [x y z] = 0$
$\Rightarrow ∣ ∣ ∣ ∣ \begin{matrix} 2 & 1 & α α & 0 & 1 5 & - 1 & 0 \end{matrix} ∣ ∣ ∣ ∣ = 0$
$\Rightarrow α = \pm \sqrt{7}$ .

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If x is parallel to y and z where x=2^i+^j+α^k,y=α^i+^k and z = 5^i−^j, then α is equal to

The correct option is C ±√7Given x is parallel to y and z ∴x.(y×z)=0⇒[x y z]=0 ⇒∣∣ ∣∣21αα015−10∣∣ ∣∣=0 ⇒α=±√7.

If $x$ is parallel to $y$ and $z$ where $x = 2^i +^j + α^k, y = α^i +^k$ and $z = 5^i -^j,$ then $α$ is equal to

The correct option is C $\pm \sqrt{7}$
Given $x$ is parallel to $y$ and $z$
$∴ x . (y \times z) = 0 \Rightarrow [x y z] = 0$
$\Rightarrow ∣ ∣ ∣ ∣ \begin{matrix} 2 & 1 & α α & 0 & 1 5 & - 1 & 0 \end{matrix} ∣ ∣ ∣ ∣ = 0$
$\Rightarrow α = \pm \sqrt{7}$ .