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I don't know, You tell me.
Use trigonometry.
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.
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.
The magnitude alone can't tell you anything about its components. You also need to know its direction.
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)
The magnitude of a vector can be found by taking the square root of each of the vector components squared. For example, if you had the vector 3i+4j, to find the magnitude, you take sqrt ( 3²+4² ) To get: sqrt ( 9+16 ) sqrt ( 25 ) = 5 Works the same in 3D or more, just put all the vector components in.
Measuring a vector requires a reference. You'll need something that will allow you to find direction, and a unit length so you can find magnitude. A graph is a good way to do this, and something with a standard x and y axis (Cartesian coordinates) is just the ticket. Our graph has an origin, and that can be your starting point. Starting there, and using the x-axis as zero degrees, find your angle. Then draw a segment out along that axis the appropriate length. You now have a vector with its angle (direction) and length (magnitude).
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