
Write two different vectors having the same magnitude.
Answer
488.4k+ views
Hint:
Here we will assume two vectors such that they have the same magnitude. It is not necessary that two vectors having the same magnitude will have the same direction. If two vectors have the same magnitude and same direction, then those vectors are called equal vectors.
Complete step by step solution:
Here we have to write vectors which have the same magnitude.
Let the first vector be and the second vector be .
We know magnitude of any vector is represented by and it is equal to .
Therefore, magnitude of vector can be represented as .
Thus,
On further simplifying the terms, we get
On adding the terms, we get
Thus, the magnitude of the vector is .
Now, we will find the magnitude of the vector
Therefore, magnitude of vector can be represented as .
Thus,
On further simplifying the terms, we get
Adding the terms, we get
Thus, the magnitude of the vector is .
Hence, the magnitude of vector and vector are equal.
Thus, the required two vectors having same magnitude are and .
Note:
If two vectors have the same magnitude, they may or may not be equal because for two vectors to be equal, they must have the same direction as well. We can say that equal vectors are vectors which have the same magnitude as well as the same direction. Here in this question also, these two vectors have the same magnitude but they do not have the same direction.
Some important properties of vectors are:-
1) To add the two vectors, we always consider both their magnitudes and directions.
2) Negative vectors are those whose direction is just opposite to the reference positive direction.
Here we will assume two vectors such that they have the same magnitude. It is not necessary that two vectors having the same magnitude will have the same direction. If two vectors have the same magnitude and same direction, then those vectors are called equal vectors.
Complete step by step solution:
Here we have to write vectors which have the same magnitude.
Let the first vector be
We know magnitude of any vector
Therefore, magnitude of vector
Thus,
On further simplifying the terms, we get
On adding the terms, we get
Thus, the magnitude of the vector
Now, we will find the magnitude of the vector
Therefore, magnitude of vector
Thus,
On further simplifying the terms, we get
Adding the terms, we get
Thus, the magnitude of the vector
Hence, the magnitude of vector
Thus, the required two vectors having same magnitude are
Note:
If two vectors have the same magnitude, they may or may not be equal because for two vectors to be equal, they must have the same direction as well. We can say that equal vectors are vectors which have the same magnitude as well as the same direction. Here in this question also, these two vectors have the same magnitude but they do not have the same direction.
Some important properties of vectors are:-
1) To add the two vectors, we always consider both their magnitudes and directions.
2) Negative vectors are those whose direction is just opposite to the reference positive direction.
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