Let p = 2i + 3j + k and q = i + 2j + k be two vectors. If a vector r = (αi + βj + γk) is perpendicular to each of the vectors (p + q) and (p - q), and |r| = √3, then |α| + |β| + |γ| is equal to……

p = 2i + 3j + k, q = I + 2j + k
r = αi + βj + γk is ⊥ to p+q and p-q
∴ r is collinear with (p+q) * (p-q) = -2 (p*q)
p*q = |i, j, k; 2,3,1; 1,2,1| = I - j + k
∴ r = λ (i - j + k)
|r| = √3 ⇒ λ = 1
∴ r = I - j + k = αi + βj + γk
⇒ α=1, β=-1, γ=1
|α|+|β|+|γ| = 3