   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 Given (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 = (𝟓𝒂 ⃗)/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 ⃗

Examples

About the Author 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.