Joining two points

Chapter 10 Class 12 Vector Algebra
Concept wise

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Ex 10.2, 8 Find the unit vector in the direction of vector (ππ) β , where P and Q are the points (1, 2, 3) and (4, 5, 6); respectively.P (1, 2, 3) Q (4, 5, 6) (ππ) β = (4 β 1) π Μ + (5 β 2) π Μ + (6 β 3) π Μ = 3π Μ + 3π Μ + 3π Μ β΄ Vector joining P and Q is given by (ππ) β = 3π Μ + 3π Μ + 3π Μ Magnitude of (ππ) β = β(32+32+32) |(ππ) β | = β(9+9+9) = β27 = 3β3 Unit vector in direction of (ππ) β = 1/(ππππππ‘π’ππ ππ (ππ) β ) Γ(ππ) β = 1/(3β3) ["3" i Μ" + 3" j Μ" + 3" k Μ ] = 3/(3β3) π Μ + 3/(3β3) π Μ + 3/(3β3) π Μ = π/βπ π Μ + π/βπ π Μ + π/βπ π Μ Thus, unit vector in direction of (ππ) β = 1/β3 π Μ + 1/β3 π Μ + 1/β3 π Μ