Question

if vector A and B are such that |A+B| =|A|=|B| then |A-B| can be equated as​

Answer 1

Answer:

|A-B| = √3a

Explanation:

Given

|A+B| = |A| = |B|

To Find

|A-B|

Solution

let,

|A| = a, |B| = b

we know that

(a+b)² = (a+b)(a+b)

(a+b)² = a²+b²+2ab

a² = a²+a²+2ab

a² = 2a²+2ab

2ab = a²-2a²

2ab = -a²

ab= $\dfrac{-1}{2}$a²

Now,

(a-b)² = (a-b)(a-b)

(a-b)² = a²+b²-2ab

(a-b)² = a²+a²-2($\dfrac{-1}{2}$a²)

(a-b)² = 2a²+a²

(a-b)² = 3a²

a-b = √3a

Hence

|A-B| = √3a