Question

if magnitude of sum of two unit vectors is √2 then find the magnitude of substraction of these unit vector

Answer 1

Let a and b be two unit vectors such that,

| a | = | b | = 1, and | a + b | = √2 . We know that

| a + b | = [ a² + b² + 2 |a | |b | Cos ß ]^½ =√2

==> [1² + 1² + 2×1×1 Cos ß]^½ = √2

Squaring both sides and transposing rhs to lhs we get

==> [ 2 + 2 Cos ß - 2]= 0

==> 2 Cos ß =0, ==> ß = 90°

| a - b | = [ 1² + 1²- 2 ×1×1× Cos ß]^½= [ 2 - 2 Cos 90°]^½ = [ 2 - 0]^½ = √2

So magnitude of difference of two unit vectors at right angles to each other is √2.