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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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