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

If $\to r \times \to b = \to c \times \to b$ and $\to r . \to a = 0$ where $\to a = 2^i + 3^j -^k, \to b = 3^i -^j +^k$ and $\to c =^i +^j + 3^k$ , then $\to r$ is equal to

Q. If

\to a =^i + 2^j + 3^k

\to b = 2^i -^j +^k

and

\to c = 3^i + 2^j +^k

and

\to a \times (\to b \times \to c)

is equal to

x \to a + y \to b + z \to c

, then

x + y + z

is equal to

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