haruspex said:
Yes, but not because you are told the answer must be in terms of b. You know from the diagram that it must be in the direction of b. Unless a and b are in the same direction, how else will you get (2/3)a + t( (-1/15)a + (2/5)b) to be a scalar multiple of b?Eysz said:
haruspex said:
Vectors are mathematical quantities that have both magnitude (size) and direction. In physics, vectors are used to represent physical quantities such as displacement, velocity, and force. They are also used to solve problems involving motion and forces.
In vector equations, OR and OP represent the position vectors of two points in space. OR is the vector from the origin to a specific point, while OP is the vector from the origin to a different point. OR and OP have the same direction, but may have different magnitudes.
To solve vector equations involving OR and OP, you can use the properties of vectors such as commutativity, associativity, and distributivity. You can also use trigonometric functions and the Pythagorean theorem to find the magnitude and direction of the resulting vector.
One example of a vector equation involving OR and OP is OR + OP = RQ. This equation represents the vector addition of OR and OP resulting in the vector RQ, which is the displacement from the origin to a point Q.
Vectors are used in various real-life applications such as navigation, engineering, and video game programming. For example, in navigation, vectors are used to represent the direction and magnitude of an aircraft's velocity. In engineering, vectors are used to analyze forces and moments acting on structures. In video game programming, vectors are used to simulate motion and collisions of objects.