Final answer:
Directly adding magnitudes of vectors to find the resultant vector's magnitude is false unless the vectors are in the same direction or at right angles. The magnitude and direction of a resultant vector are influenced by both the magnitudes and directions of the individual vectors, which must be considered through trigonometry or graphical methods.
Step-by-step explanation:
When finding the magnitude of the sum of two vectors, you cannot directly add the magnitudes of the two vectors. This is False. The correct way of calculating the magnitude of the sum involves taking into consideration both the magnitudes and the directions of the vectors. For vectors that are at a right angle to each other, you can use the Pythagorean theorem to calculate the length of the resultant vector. However, in other cases, you may need to apply trigonometry and vector addition rules to compute the correct magnitude and direction.
For instance:
- If both vectors point in the same direction, their magnitudes can be directly added.
- If the vectors are at a right angle, use the Pythagorean theorem to find the magnitude of the resultant vector.
If you know the angles of two vectors and the magnitude of one, you can indeed find the magnitude and direction of the resultant vector, although it typically requires using trigonometric methods or graphical representation. Additionally, just knowing the angles may not be sufficient to find the angle of the resultant vector unless magnitudes are also known. The resultant vector's direction depends on both the magnitude and direction of the added vectors. If you add several vectors, the magnitude of their sum is not simply the sum of individual magnitudes; the order and direction each vector points play a crucial role.