If x is parallel to y and z where x-2 - k- y-k- and z-5 - then - is equal to A- -7B- None of these C- -5D- -6

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

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Standard IX

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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N o n e o f t h e s e

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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+αk,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⇒[xyz]=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
$∴ x . (y \times z) = 0 \Rightarrow [x y z] = 0$
$\Rightarrow ∣ ∣ ∣ ∣ \begin{matrix} 2 & 1 & α α & 0 & 1 5 & - 1 & 0 \end{matrix} ∣ ∣ ∣ ∣ = 0 \Rightarrow α \pm \sqrt{7}$ .