Let `veca=hati-hatk, vecb=xhati+hatj+(1-x)hatk` and `vecc=yhati+xhatj+(1+x-y)hatk`, then `[veca vecb vecc]` depends on

Options

A. only `x`
B. only `y`
C. neither `x` nor `y`
D. both `x` and `y`

Explanation

To solve the problem, we need to determine the scalar triple product of the vectors \( \vec{a} \), \( \vec{b} \), and \( \vec{c} \). The scalar triple product can be calculated using the determinant of a matrix formed by these vectors. Let's go through the steps systematically.

### Step 1: Define the Vectors
We start by defining the vectors as given in the problem.

\[ \vec{a} = \hat{i} - \hat{k} \]
...