Question:
The vector with terminal point A (2, -3, 5) and initial point B (3, -4, 7) is:
The vector with terminal point A (2, -3, 5) and initial point B (3, -4, 7) is:
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To find a vector between two points, subtract the coordinates of the initial point from the terminal point.
Updated On: Feb 27, 2025
- \( \hat{i} - \hat{j} + 2\hat{k} \)
- \( \hat{i} + \hat{j} + 2\hat{k} \)
- \( -\hat{i} - \hat{j} - 2\hat{k} \)
- \( -\hat{i} + \hat{j} - 2\hat{k} \)
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The Correct Option is C
Solution and Explanation
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:
\[
\boxed{-\hat{i} - \hat{j} - 2\hat{k}}
\]
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