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.
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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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.
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.
We get the Unit Vector
The magnitude of a vector is a geometrical value for hypotenuse.. The magnitude is found by taking the square root of the i and j components.
Suppose the magnitude of the vector is V and its direction makes an angle A with the x-axis, then the x component is V*Cos(A) and the y component is V*Sin(A)
One component = (magnitude) times (cosine of the angle).Other component = (magnitude) times (sine of the angle).In order to decide which is which, we have to know the angle with respect to what.