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In triangle ABC, the side vectors are AB = 3i + 4k and AC = 5i − 2j + 4k. What is the magnitude of the median drawn from vertex A?

1. √388
2. √18
3. √72
4. √33

Correct answer: √33

Solution

The median from vertex A to side BC can be calculated using the formula for the length of a median in a triangle, which involves the lengths of the sides and the coordinates of the vertices. By finding the midpoint of side BC and then calculating the distance from vertex A to this midpoint, we find that the magnitude of the median is √33.

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