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Find the unit vector in the direction of vector PQ, where P and Q are

Ex 10.2, 8 - Chapter 10 Class 12 Vector Algebra - Part 2

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Ex 10.2, 8 Find the unit vector in the direction of vector (𝑃𝑄) βƒ— , where P and Q are the points (1, 2, 3) and (4, 5, 6); respectively.P (1, 2, 3) Q (4, 5, 6) (𝑃𝑄) βƒ— = (4 – 1) 𝑖 Μ‚ + (5 – 2) 𝑗 Μ‚ + (6 – 3) π‘˜ Μ‚ = 3𝑖 Μ‚ + 3𝑗 Μ‚ + 3π‘˜ Μ‚ ∴ Vector joining P and Q is given by (𝑃𝑄) βƒ— = 3𝑖 Μ‚ + 3𝑗 Μ‚ + 3π‘˜ Μ‚ Magnitude of (𝑃𝑄) βƒ— = √(32+32+32) |(𝑃𝑄) βƒ— | = √(9+9+9) = √27 = 3√3 Unit vector in direction of (𝑃𝑄) βƒ— = 1/(π‘šπ‘Žπ‘”π‘›π‘–π‘‘π‘’π‘‘π‘’ π‘œπ‘“ (𝑃𝑄) βƒ— ) Γ—(𝑃𝑄) βƒ— = 1/(3√3) ["3" i Μ‚" + 3" j Μ‚" + 3" k Μ‚ ] = 3/(3√3) 𝑖 Μ‚ + 3/(3√3) 𝑗 Μ‚ + 3/(3√3) π‘˜ Μ‚ = 𝟏/βˆšπŸ‘ π’Š Μ‚ + 𝟏/βˆšπŸ‘ 𝒋 Μ‚ + 𝟏/βˆšπŸ‘ π’Œ Μ‚ Thus, unit vector in direction of (𝑃𝑄) βƒ— = 1/√3 𝑖 Μ‚ + 1/√3 𝑗 Μ‚ + 1/√3 π‘˜ Μ‚

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