Question

if [A+B]=[A-B] then prove that A and B are perpendicular to each other.​

Answer 1

Answer:

f [A+B]=[A-B] then prove that A and B are perpendicular to each other.

Answer 2

$\huge\red{\underline{{\boxed{\textbf{QUESTION}}}}}$

If [A+B]=[A-B] then prove that A and B are perpendicular to each other.

$\huge\red{\underline{{\boxed{\textbf{ANSWER}}}}}$

∥a⃗ +b⃗ ∥=∥a⃗ −b⃗ ∥

Dotting a vector with itself is the square of its length:

∥a⃗ +b⃗ ∥2=∥a⃗ −b⃗ ∥2

(a⃗ +b⃗ )⋅(a⃗ +b⃗ )=(a⃗ −b⃗ )⋅(a⃗ −b⃗ )

Dot product distributes over addition:

a⃗ ⋅(a⃗ +b⃗ )+b⃗ ⋅(a⃗ +b⃗ )=a⃗ ⋅(a⃗ −b⃗ )−b⃗ ⋅(a⃗ −b⃗ )

a⃗ ⋅a⃗ +2a⃗ ⋅b⃗ +b⃗ ⋅b⃗ =a⃗ ⋅a⃗ −2a⃗ ⋅b⃗ +b⃗ ⋅b⃗

2(a⃗ ⋅b⃗ )=−2(a⃗ ⋅b⃗ )

a⃗ ⋅b⃗ =0

Vectors dot to 0 iff they are perpendicular:

a⃗ is perpendicular to b⃗

@HarshPratapSingh