If the vectors AB → = 3 i ^ + 4 k ^ and AC → = 5 i ^ - 2 j ^ + 4 k ^ are the sides of a triangle A B C , then the length of the median through A is:

Length of median = AB → + AC → 2 = 8 i ^ - 2 j ^ + 8 k ^ 2 = 3 3

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MathematicsVectorGeneral definitions, Angle between vectors, Section formula, Geometrical resultsHard2 minPYQ_2013

MathematicsHardsingle choice

If the vectors $\vec{AB} = 3 \hat{i} + 4 \hat{k}$ and $\vec{AC} = 5 \hat{i} - 2 \hat{j} + 4 \hat{k}$ are the sides of a triangle $A B C,$ then the length of the median through $A$ is:

Question diagram: If the vectors AB → = 3 i ^ + 4 k ^ and AC → = 5 i ^ - 2 j ^

Options:

Answer:

Solution:

Length of median $= |\frac{\vec{AB} + \vec{AC}}{2}|$

$= |\frac{8 \hat{i} - 2 \hat{j} + 8 \hat{k}}{2}|$

$= \sqrt{33}$

Stream:JEESubject:MathematicsTopic:VectorSubtopic:General definitions, Angle between vectors, Section formula, Geometrical results

⏱ 2mℹ️ Source: PYQ_2013

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