The vectors AB = 3i + 4k and AC = 5i - 2j + 4k are the sides of a triangle ABC . The length of the median through A is: - Mathematics MCQ Mathematics Mock Test - 9 2026 | ExamTest.live

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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 . The length of the median through A is:

Solution & Step-by-step Explanation

Let m be the median from A to the midpoint of BC . The position vector of the median is given by: m = \frac{A B + A C}{2} m = \frac{( 3 i ^ + 4 k ^ ) + ( 5 i ^ - 2 j ^ + 4 k ^ )}{2} m = \frac{8 i ^ - 2 j ^ + 8 k ^}{2} = 4 \hat{i} - \hat{j} + 4 \hat{k} Length of median ∣ m ∣ = 4^{2} + (- 1)^{2} + 4^{2} = 16 + 1 + 16 = 33 .

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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 . The length of the median through A is:

18

72

33

288

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