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1. Chapter 10 Class 12 Vector Algebra
2. Serial order wise
3. Examples

Transcript

Example 11 Consider two points P and Q with position vectors (𝑂𝑃) ⃗ = 3𝑎 ⃗ − 2𝑏 ⃗ and (𝑂𝑄) ⃗ = 𝑎 ⃗ + 𝑏 ⃗ . Find the position vector of a point R which divides the line joining P and Q in the ratio 2 : 1, (i) internally, and (𝑂𝑃) ⃗ = 3𝑎 ⃗ − 2𝑏 ⃗ (𝑂𝑄) ⃗ = 𝑎 ⃗ + 𝑏 ⃗ Position vector of R = (2(𝑂𝑄) ⃗ + 1(𝑂𝑃) ⃗)/(2 + 1) (𝑂𝑅) ⃗ = (2(𝑎 ⃗ + 𝑏 ⃗ ) + 1(3𝑎 ⃗ − 2𝑏 ⃗ ))/(2 + 1) = (2𝑎 ⃗ + 2𝑏 ⃗ + 3𝑎 ⃗ − 2𝑏 ⃗)/3 ] Thus, position vector of R dividing P and Q internally is (5𝑎 ⃗)/3. Example 11 Consider two points P and Q with position vectors (𝑂𝑃) ⃗ = 3𝑎 ⃗ − 2𝑏 ⃗ and (𝑂𝑄) ⃗ = 𝑎 ⃗ + 𝑏 ⃗ . Find the position vector of a point R which divides the line joining P and Q in the ratio 2 : 1, (ii) externally. Position vector of R = (2(𝑂𝑄) ⃗ − 1(𝑂𝑃) ⃗)/(𝟐 − 𝟏) (𝑂𝑅) ⃗ = (2(𝑎 ⃗ + 𝑏 ⃗ ) − 1(3𝑎 ⃗ − 2𝑏 ⃗))/(2 − 1) = (2𝑎 ⃗ + 2𝑏 ⃗ − 3𝑎 ⃗ + 2𝑏 ⃗)/1 = −𝑎 ⃗ + 4𝑏 ⃗ = 4𝒃 ⃗ − 𝒂 ⃗ Thus, position vector of R dividing P and Q externally is 4𝑏 ⃗ – 𝑎 ⃗

Examples 