Section formula

Chapter 10 Class 12 Vector Algebra
Concept wise

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Ex 10.2, 16 Find the position vector of the mid point of the vector joining the points P(2, 3, 4) and Q(4, 1, β2). P(2, 3, 4) , Q(4, 1, β2) Let the midpoint of PQ be R. Position vector of P = (2 β 0) π Μ + (3 β 0) π Μ + (4 β 0) π Μ (ππ) β = 2π Μ + 3π Μ + 4π Μ Position vector of Q = (4 β 0) π Μ + (1 β 0) π Μ + (β2 β 0) π Μ (ππ) β = 4π Μ + 1π Μ β 2π Μ Position vector of R = ((πΆπΈ) β + (πΆπ·) β)/π (ππ) β = ((4π Μ + 1π Μ β 2π Μ ) + (2π Μ + 3π Μ + 4π Μ))/2 (ππ) β = ((4 + 2) π Μ + (1 + 3) π Μ + (β2 + 4)π Μ)/2 (ππ) β = (6π Μ + 4π Μ + 2π Μ)/2 (ππ) β = (2(3π Μ + 2π Μ + π Μ))/2 (ππ) β = ππ Μ+ππ Μ+π Μ Therefore, position vector of midpoint of PQ is 3π Μ + 2π Μ + π Μ