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Question: Let <img src="https://cdn.pureessence.tech/canvas_356.png?top_left_x=704&top_left_y=1361&width=300&h...

Let ,c=yi+xj+(1+x−y)k\mathbf { c } = y \mathbf { i } + x \mathbf { j } + ( 1 + x - y ) \mathbf { k }.

Then depends on

A

Only x

B

Only y

C

Neither x nor y

D

Both x and y

Answer

Neither x nor y

Explanation

Solution

[abc]=∣10−1x11−xyx1+x−y∣=∣100x11yx1+x∣=∣11x1+x∣=1[ \mathbf { a } \mathbf { b } \mathbf { c } ] = \left| \begin{array} { c c c } 1 & 0 & - 1 \\ x & 1 & 1 - x \\ y & x & 1 + x - y \end{array} \right| = \left| \begin{array} { c c c } 1 & 0 & 0 \\ x & 1 & 1 \\ y & x & 1 + x \end{array} \right| = \left| \begin{array} { c c } 1 & 1 \\ x & 1 + x \end{array} \right| = 1 .