if magnitude of sum of two unit vectors is root2 then find the magnitude of subtraction of these unit vectors
Root 2
To find the magnitude of the subtraction of two unit vectors given that the magnitude of their sum is √2, we can use the Pythagorean theorem and some vector properties.
Let's assume the two unit vectors as A and B.
1. The magnitude of a unit vector is always 1. So, the magnitude of vector A is 1 and the magnitude of vector B is also 1.
2. The magnitude of the sum of these two vectors, denoted as vector C, is given as √2.
3. Using the Pythagorean theorem, the magnitude of the vector C can be expressed as:
|C|² = |A|² + |B|²
Since |A| = 1 and |B| = 1, we have:
|C|² = 1² + 1²
|C|² = 2
Therefore, the magnitude of C, |C|, is equal to √2.
4. Now, we need to find the magnitude of the subtraction of these unit vectors, denoted as vector D. Mathematically, it can be expressed as:
D = A - B
|D| = |A - B|
5. To calculate |D|, we need to consider the properties of vector subtraction. Vector subtraction is equivalent to vector addition with the negative of the vector being subtracted. So, we can rewrite the equation as:
|D| = |A + (-B)|
|D| = |C|
Since we already found that |C| is √2, the magnitude of the subtraction of these unit vectors is also √2.
Therefore, the magnitude of the subtraction of the two unit vectors is √2.