Let a-k- b-x-1-xk-c-y-x-1-x-yk- then -abc- depends on

The correct option is D neither x nor y [abc]=[ 1 amp; 0 amp; 1 x amp;1 nbsp; amp;1 x nbsp; y amp; x amp; 1+ ...

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Byju's Answer

Standard XII

Mathematics

Addition of Vectors

Let a=î-k̂,...

Question

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

only

x

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only

y

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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 D neither $x$ nor $y$
$[\to a \to b \to c] = ⎡ ⎢ ⎣ \begin{matrix} 1 & 0 & - 1 x & 1 & 1 - x y & x & 1 + x - y \end{matrix} ⎤ ⎥ ⎦$
$c_{1} + c_{2} \to c_{3}$
$= ⎡ ⎢ ⎣ \begin{matrix} 1 & 0 & - 1 + 1 x & 1 & 1 - x + x + 1 y & x & 1 + x - y + x + y \end{matrix} ⎤ ⎥ ⎦$
$= ⎡ ⎢ ⎣ \begin{matrix} 1 & 0 & 0 x & 1 & 2 y & x & 1 + 2 x \end{matrix} ⎤ ⎥ ⎦$
$= 1 (1 + 2 x - 2 x) - 0 + 0 = 1$

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

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