Ex 10.2, 16 - Find position vector of mid point of vector

Ex 10.2, 16 - Chapter 10 Class 12 Vector Algebra - Part 2

  1. Chapter 10 Class 12 Vector Algebra (Term 2)
  2. Serial order wise

Transcript

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, –2). P(2, 3, 4) , Q(4, 1, βˆ’2) Let the midpoint of PQ be R. Position vector of P = (2 βˆ’ 0) 𝑖 Μ‚ + (3 βˆ’ 0) 𝑗 Μ‚ + (4 βˆ’ 0) π‘˜ Μ‚ (𝑂𝑃) βƒ— = 2𝑖 Μ‚ + 3𝑗 Μ‚ + 4π‘˜ Μ‚ Position vector of Q = (4 βˆ’ 0) 𝑖 Μ‚ + (1 βˆ’ 0) 𝑗 Μ‚ + (βˆ’2 βˆ’ 0) π‘˜ Μ‚ (𝑂𝑄) βƒ— = 4𝑖 Μ‚ + 1𝑗 Μ‚ βˆ’ 2π‘˜ Μ‚ Position vector of R = ((𝑢𝑸) βƒ— + (𝑢𝑷) βƒ—)/𝟐 (𝑂𝑅) βƒ— = ((4𝑖 Μ‚ + 1𝑗 Μ‚ βˆ’ 2π‘˜ Μ‚ ) + (2𝑖 Μ‚ + 3𝑗 Μ‚ + 4π‘˜ Μ‚))/2 (𝑂𝑅) βƒ— = ((4 + 2) 𝑖 Μ‚ + (1 + 3) 𝑗 Μ‚ + (βˆ’2 + 4)π‘˜ Μ‚)/2 (𝑂𝑅) βƒ— = (6𝑖 Μ‚ + 4𝑗 Μ‚ + 2π‘˜ Μ‚)/2 (𝑂𝑅) βƒ— = (2(3𝑖 Μ‚ + 2𝑗 Μ‚ + π‘˜ Μ‚))/2 (𝑂𝑅) βƒ— = πŸ‘π’Š Μ‚+πŸπ’‹ Μ‚+π’Œ Μ‚ Therefore, position vector of midpoint of PQ is 3𝑖 Μ‚ + 2𝑗 Μ‚ + π‘˜ Μ‚

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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 10 years. He provides courses for Maths and Science at Teachoo.