Section formula
Last updated at April 16, 2024 by Teachoo
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, β2). P(2, 3, 4) , Q(4, 1, β2) 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 (ππ) β = 2π Μ + 3π Μ + 4π Μ Position vector of Q = (4 β 0) π Μ + (1 β 0) π Μ + (β2 β 0) π Μ (ππ) β = 4π Μ + 1π Μ β 2π Μ Position vector of R = ((πΆπΈ) β + (πΆπ·) β)/π (ππ ) β = ((4π Μ + 1π Μ β 2π Μ ) + (2π Μ + 3π Μ + 4π Μ))/2 (ππ ) β = ((4 + 2) π Μ + (1 + 3) π Μ + (β2 + 4)π Μ)/2 (ππ ) β = (6π Μ + 4π Μ + 2π Μ)/2 (ππ ) β = (2(3π Μ + 2π Μ + π Μ))/2 (ππ ) β = ππ Μ+ππ Μ+π Μ Therefore, position vector of midpoint of PQ is 3π Μ + 2π Μ + π Μ