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

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

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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, –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 has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.