The vector from \( B(3, -4, 7) \) to \( A(2, -3, 5) \) is given by: \[ \overrightarrow{BA} = (x_2 - x_1)\hat{i} + (y_2 - y_1)\hat{j} + (z_2 - z_1)\hat{k}, \] where \( (x_1, y_1, z_1) \) are the coordinates of point \( B \), and \( (x_2, y_2, z_2) \) are the coordinates of point \( A \).
Substituting the given coordinates: \[ \overrightarrow{BA} = (2 - 3)\hat{i} + (-3 - (-4))\hat{j} + (5 - 7)\hat{k}. \]
Simplify each term: \[ \overrightarrow{BA} = (-1)\hat{i} + (1)\hat{j} + (-2)\hat{k}. \]
Thus: \[ \overrightarrow{BA} = -\hat{i} + \hat{j} - 2\hat{k}. \]
Hence, the vector is \(-\hat{i} + \hat{j} - 2\hat{k}\), and the correct answer is (D).
Arrange the following states in sequence (highest to lowest) according to their reserves of iron ore and choose the correct option.
I. Jharkhand
II. Karnataka
III. Chhattisgarh
IV. Odisha