Question:
If \(O\) is the origin and \(C\) is the midpoint of \(A(-2,1)\) and \(B(4,-3)\), then \(\vec{OC}\) is:
If \(O\) is the origin and \(C\) is the midpoint of \(A(-2,1)\) and \(B(4,-3)\), then \(\vec{OC}\) is:
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Position vector is same as coordinates from origin.
Updated On: Apr 30, 2026
- \(\hat{i} + \hat{j} \)
- \(-\hat{i} + \hat{j} \)
- \(\frac{1}{2}\hat{i} + \frac{1}{2}\hat{j} \)
- \(\hat{i} - \hat{j} \)
- \(-\hat{i} - \hat{j} \)
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The Correct Option is D
Solution and Explanation
Concept:
Midpoint formula:
\[
C = \left(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}\right)
\]
Step 1: Find midpoint.
\[ C = \left(\frac{-2+4}{2}, \frac{1-3}{2}\right) = (1,-1) \]
Step 2: Position vector.
\[ \vec{OC} = \hat{i} - \hat{j} \]
Step 1: Find midpoint.
\[ C = \left(\frac{-2+4}{2}, \frac{1-3}{2}\right) = (1,-1) \]
Step 2: Position vector.
\[ \vec{OC} = \hat{i} - \hat{j} \]
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