Question

The vector with terminal point A (2, -3, 5) and initial point B (3, -4, 7) is:

• A. \( \hat{i} - \hat{j} + 2\hat{k} \)
• B. \( \hat{i} + \hat{j} + 2\hat{k} \)
• C. \( -\hat{i} - \hat{j} - 2\hat{k} \)
• D. \( -\hat{i} + \hat{j} - 2\hat{k} \)

Hint:

To find a vector between two points, subtract the coordinates of the initial point from the terminal point.

Answer 1

The Correct Option is C

Step 1: Apply the vector formula. \[ \vec{AB} = (x_2 - x_1)\hat{i} + (y_2 - y_1)\hat{j} + (z_2 - z_1)\hat{k} \] Substituting values \( A(2, -3, 5) \) and \( B(3, -4, 7) \): \[ \vec{AB} = (2 - 3)\hat{i} + (-3 + 4)\hat{j} + (5 - 7)\hat{k} \] Step 2: Simplify the components. \[ \vec{AB} = -\hat{i} - \hat{j} - 2\hat{k} \] Final Answer: \[ \boxed{-\hat{i} - \hat{j} - 2\hat{k}} \]