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Let ABCD be a parallelogram such that AB = q, AD = p and ∠DAB an acute angle. If r is the vector that coincide with the altitude directed from the vertex B to the side AD, then r is given by:

1. r = 3q - 3((p·q)/(p·p)) p
2. r = -q + ((p·q)/(p·p)) p
3. r = q - ((p·q)/(p·p)) p
4. r = -3q - 3((p·q)/(p·p)) p

Correct answer: r = -q + ((p·q)/(p·p)) p

Solution

The correct option represents the vector from point B to the line AD, calculated by subtracting the projection of vector q onto vector p from vector q itself. This projection accounts for the angle between the vectors, ensuring that the resultant vector r is perpendicular to AD, which is the definition of an altitude.

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