Question:
If the vectors \(\overrightarrow{AB}=3 \hat{i}+8 \hat{k}\) and \(\overrightarrow{AC}=5 \hat{i}-2 \hat{j}+6 \hat{k}\) are the sides of a triangle \(ABC\), then the length of the median through \(A\) is
If the vectors \(\overrightarrow{AB}=3 \hat{i}+8 \hat{k}\) and \(\overrightarrow{AC}=5 \hat{i}-2 \hat{j}+6 \hat{k}\) are the sides of a triangle \(ABC\), then the length of the median through \(A\) is
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The median from A to the midpoint D of BC is \(\overrightarrow{AD}=\frac{\overrightarrow{AB}+\overrightarrow{AC}}{2}\).
Updated On: Nov 12, 2026
- \(\sqrt{33}\)
- \(\sqrt{66}\)
- \(\sqrt{56}\)
- \(\sqrt{72}\)
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The Correct Option is B
Solution and Explanation
\(\overrightarrow{AD}=\frac12(\overrightarrow{AB}+\overrightarrow{AC})=\frac12(8\hat i-2\hat j+14\hat k)=4\hat i-\hat j+7\hat k\).
Length \(=\sqrt{16+1+49}=\sqrt{66}\).
Answer: (2) \(\sqrt{66}\)
Length \(=\sqrt{16+1+49}=\sqrt{66}\).
Answer: (2) \(\sqrt{66}\)
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