Question

if vector A and B has equal magnitude and A+B is 3 times larger than A-B what is the angle of A and B Search instead for if vector A and B has equal magnitude and A+B is three times larger than A-B what must be the angle of A and B

Answer 1

Let's represent the magnitude of both vectors A and B using the variable "m".

According to the problem statement, we have:

|A| = |B| = m

|A+B| = 3|A-B|

Squaring both sides, we get:

|A+B|^2 = 9|A-B|^2

Expanding the left-hand side using the dot product formula, we have:

(A+B)·(A+B) = A·A + 2A·B + B·B

Similarly, expanding the right-hand side, we have:

9(A-B)·(A-B) = 9A·A - 18A·B + 9B·B

Substituting the given magnitudes, we have:

(A+B)·(A+B) = 2m^2 + 2(A·B)

9(A-B)·(A-B) = 18m^2 - 18(A·B)

Substituting these expressions back into the original equation, we get:

2m^2 + 2(A·B) = 9(18m^2 - 18(A·B))

Simplifying and rearranging, we get:

20(A·B) = 323m^2

Dividing by |A|·|B| = m^2, we have:

20(cosθ) = 323

where θ is the angle between vectors A and B. Solving for θ, we get:

θ = cos⁻¹(323/20)/π * 180

θ ≈ 83.4 degrees