Let a-k-b-x -1-xk- and c-y-x -1-x-yk- Then -a-b-c- depends on

The correct option is C both x and y a⃗= k̂ b⃗=x î++(1 x) k̂ c⃗=y +x +(1+x y) k̂ [a⃗b⃗c⃗] amp;=|[ 0 amp; 1 amp; 1; x ...

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Byju's Answer

Standard XII

Mathematics

Skew Lines

Let a⃗=ĵ-k̂...

Question

Let $\to a =^j -^k, \to b = x^i +^j + (1 - x)^k$ and $\to c = y^i + x^j + (1 + x - y)^k$ . Then $[\to a, \to b, \to c]$ depends on

only y

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only x

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both x and y

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neither x nor y

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Solution

The correct option is C both x and y
$\to a =^ȷ -^k \to b = x^i +^ȷ + (1 - x)^k \to c = y^ı + x^ȷ + (1 + x - y)^k$
$[\to a \to b \to c]$
$\begin{matrix} = ∣ ∣ ∣ ∣ \begin{matrix} 0 & 1 & - 1 x & 1 & 1 - x y & x & 1 + x - y \end{matrix} ∣ ∣ ∣ ∣ = - 2 x^{2} + 2 y - x \end{matrix}$
$so [\to a \to b \to c] depends on both x and y$

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Let →a=^j−^k,→b=x^i+^j+(1−x)^k and →c=y^i+x^j+(1+x−y)^k. Then [→a,→b,→c] depends on

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Let $\to a =^j -^k, \to b = x^i +^j + (1 - x)^k$ and $\to c = y^i + x^j + (1 + x - y)^k$ . Then $[\to a, \to b, \to c]$ depends on