A+B+C=0out of three vector two r equal in magnitudeand magnitude of third is root 2times that of eitherof two hsving equal magnitude.than angle beteen vectors r

To find the angle between the vectors, let's break down the problem step by step:

1. Let's assume the two vectors with equal magnitudes are A and B, and the third vector with a magnitude √2 times that of A or B is C.
2. We know that the sum of these vectors is equal to 0: A + B + C = 0.
3. Since A and B have equal magnitudes, we can rewrite the equation as: 2A + C = 0.
4. Now, square both sides of the equation to eliminate the square root: (2A + C)^2 = 0.
5. Expanding the equation, we get: 4A^2 + C^2 + 4AC = 0.
6. Since A and B have equal magnitudes, we can say that A^2 = B^2.
7. Also, since the magnitude of C is √2 times that of A or B, we can say that C^2 = 2A^2 = 2B^2.
8. Substituting these values into the expanded equation, we have: 4A^2 + 2A^2 + 4AC = 0.
9. Combining like terms, we get: 6A^2 + 4AC = 0.
10. Factoring out a common term of 2A, we have: 2A(3A + 2C) = 0.
11. We have two possibilities for the equation to be true: either A = 0, or 3A + 2C = 0.
12. If A = 0, it means that both A and B are zero vectors with no magnitude, which is not what we are looking for.
13. Therefore, let's consider the second possibility: 3A + 2C = 0.
14. Rearranging the equation to solve for A, we have: A = -2C/3.
15. Now, we know that A and C are vectors with magnitudes in the ratio of 1:√2, respectively. Therefore, let A = k and C = √2k, where k is a constant.
16. Substituting the values of A and C into the equation, we have: k = -2(√2k)/3.
17. Simplifying, we get: 3k = -2√2k.
18. Dividing both sides by k (since k cannot be zero), we have: 3 = -2√2.
19. Squaring both sides of the equation, we get: 9 = 8.
20. This is a contradiction, which means our initial assumption that A and B have equal magnitudes cannot be true. Therefore, there is no valid solution for the given conditions.
21. In conclusion, there is no angle between vectors because the given conditions lead to a contradiction.