If vector B is added to vector A, under what condition does the resultant vector A  B havemagnitude A  B ? Under what conditions is the resultant vector equal to zero

The magnitude of the resultant vector A + B equals the magnitude of A + B when vectors A and B are in the same direction. This is because vectors in the same direction add up linearly, so their magnitudes also add up.

The resultant vector A + B equals zero when vectors A and B are equal in magnitude but opposite in direction. This is because vectors in opposite directions subtract from each other, so if they have the same magnitude, they will cancel each other out, resulting in a zero vector.

Statement I: When a body is thrown vertically upwards, it experiences a force of gravity pulling it downwards and air resistance pushing it upwards. This means that the body will take longer to reach its peak height than it would if there was no air resistance. On the other hand, when the body is falling, both gravity and air resistance are acting in the same direction (downwards), so the body falls faster than it rose. Therefore, the time during which the body rises is greater than the time of fall.

Statement II: The acceleration of a body thrown vertically upwards is always the same, regardless of its position. This is because the acceleration is due to gravity, which is a constant force. Even when the body reaches half of its maximum height, the acceleration remains the same. However, the velocity of the body decreases as it rises due to the opposing force of gravity.