Distance of the point P(p⃗ ) from the line r⃗ =a⃗ +λb⃗  is

[c] Let Q (q⃗ ) be the foot of altitude drawn from P(p⃗ ) to the line r⃗ =a⃗ +λb⃗ , ⇒(q⃗ −p⃗ ).b⃗ =0 and q⃗ =a⃗ +λb⃗  ⇒(a⃗ +λb⃗ −p⃗ ).b⃗ =0 or |(a⃗ −p⃗ )|.b⃗ +λ∣∣b⃗ ∣∣2=0 or λ=(p⃗ −a⃗ ).b⃗ )b⃗ ∣∣b⃗ ∣∣2−P⃗  ⇒|q⃗ −p⃗ |=∣∣∣∣(a⃗ −p⃗ )+(p⃗ −a⃗ ).b⃗ )b⃗ ∣∣b⃗ ∣∣2∣∣∣∣