Final answer:
The dot product of two vectors with an angle less than 90° is a positive number because the cosine of the angle is positive, which results in a positive product when calculating the dot product.
Step-by-step explanation:
The dot product of two vectors with an angle between them that is less than 90° is always a positive number. When the angle (φ) between the two vectors is between 0° and 90°, the cosine of this angle is positive, which follows from the properties of the trigonometric cosine function. Since the dot product is calculated as the product of the vectors' magnitudes and the cosine of the angle between them (A · B = AB cos φ), a positive cosine will result in a positive dot product.
If the angle is precisely 0°, the vectors are parallel, and the dot product is simply the product of their magnitudes, which is also positive. In contrast, when vectors are perpendicular (at 90°), the dot product is zero because the cosine of 90° is zero. It is important to distinguish between the dot product and the cross product, which will have a different outcome and should not be confused with one another.