If the vectors AB = 3i + 4k and AC = 5i - 2j + 4k are the sides of a triangle ABC , then the length of the median through A is: - Mathematics MCQ JEE Main 2026 | ExamTest.live

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

Solution & Step-by-step Explanation

Let the median through A be A M . M is the midpoint of side BC .In △ A BC, A M = \frac{A B + A C}{2} . A M = \frac{( 3 i ^ + 4 k ^ ) + ( 5 i ^ - 2 j ^ + 4 k ^ )}{2} = \frac{8 i ^ - 2 j ^ + 8 k ^}{2} = 4 \hat{i} - \hat{j} + 4 \hat{k} Length of median ∣ A M ∣ = 4^{2} + (- 1)^{2} + 4^{2} = 16 + 1 + 16 = 33 .

Try it yourself before checking the explanation above.

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

\sqrt{72}

\sqrt{33}

\sqrt{45}

18

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