A necessary and sufficient condition for (λ a + b) ⊥ (a - λ b) given vector a = (1,2), B = (- 2,1)

A necessary and sufficient condition for (λ a + b) ⊥ (a - λ b) given vector a = (1,2), B = (- 2,1)

(λa+b)⊥(a-b)
λa+b=（λ-2,2λ+1） a-b=（3,1）
We get 3 (λ - 2) + 2 λ + 1 = 0
We get λ = 1
So the necessary and sufficient condition is λ = 1

College entrance examination mathematics: give the following proposition: 1.0 vector a = 0; 2. Vector a = vector B if and only if | vector a | = | vector B | and vector A / / vector B
The following propositions are given
0 vector a = 0;
2. If and only if vector a = vector B is | vector a | = | vector B | and vector A / / vector B;
3. If both vectors a and B are nonzero vectors, then | vector a + vector B | and | vector a + | vector B | must be equal,
The number of the correct proposition is ()
Online, etc

First, a number multiplied by a vector is a vector, so it's a zero vector. Second, it's not necessary, so it's wrong. Third, you can draw a graph or take a number