You can't derive the direction only from the magnitude. A vector with the same magnitude can have different directions. You need some additional information to make conclusions about the direction.
You can't derive the direction only from the magnitude. A vector with the same magnitude can have different directions. You need some additional information to make conclusions about the direction.
You can't derive the direction only from the magnitude. A vector with the same magnitude can have different directions. You need some additional information to make conclusions about the direction.
You can't derive the direction only from the magnitude. A vector with the same magnitude can have different directions. You need some additional information to make conclusions about the direction.
That's it! You know everything there is to know about it. It's not as if you have to wander through a crowd of vectors and find one that matches the description. "Find the vector" means figure out its magnitude and direction. If the problem already gave you the magnitude and direction, then it's unlikely that it's asking you to 'find' that same vector.
The magnitude alone can't tell you anything about its components. You also need to know its direction.
Use trigonometry.
Given a vector, speed is the magnitude of the velocity vector, |v|. Consider vector V= IVx + JVy + KVz the magnitude is |V| = ( Vx2 + Vy2 + Vz2)1/2
If they are parallel, you can add them algebraically to get a resultant vector. Then you can resolve the resultant vector to obtain the vector components.
Divide the vector by it's length (magnitude).
That's it! You know everything there is to know about it. It's not as if you have to wander through a crowd of vectors and find one that matches the description. "Find the vector" means figure out its magnitude and direction. If the problem already gave you the magnitude and direction, then it's unlikely that it's asking you to 'find' that same vector.
The magnitude alone can't tell you anything about its components. You also need to know its direction.
Use trigonometry.
Given a vector, speed is the magnitude of the velocity vector, |v|. Consider vector V= IVx + JVy + KVz the magnitude is |V| = ( Vx2 + Vy2 + Vz2)1/2
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To add two vectors, place the tail of the second vector at the head of the first vector. The sum of the two vectors is the vector that connects the tail of the first vector to the head of the second vector. Calculate its magnitude and direction if needed.
The order in which vectors are combined affects the overall displacement because vector addition is not commutative. The resultant vector will be different depending on the direction and magnitude of each individual vector. To find the total displacement, you must consider both the direction and magnitude of each vector in relation to the others.
If they are parallel, you can add them algebraically to get a resultant vector. Then you can resolve the resultant vector to obtain the vector components.
We get the Unit Vector
The magnitude of (i + 2j) is sqrt(5). The magnitude of your new vector is 2. If both vectors are in the same direction, then each component of one vector is in the same ratio to the corresponding component of the other one. The components of the known vector are 1 and 2, and its magnitude is sqrt(5). The magnitude of the new one is 2/sqrt(5) times the magnitude of the old one. So its x-component is 2/sqrt(5) times i, and its y-component is 2/sqrt(5) times 2j. The new vector is [ (2/sqrt(5))i + (4/sqrt(5))j ]. Since the components of both vectors are proportional, they're in the same direction.
They can be represented by a line made with a #2 pencil. The length of the line is made proportional to the magnitude of the vector, and some kind of identifying mark is made on or near one end of the line to show the direction of the vector.