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 ๐๐๏ทฏ = 3 ๐๏ทฏ โ 2 ๐๏ทฏ and ๐๐๏ทฏ = ๐๏ทฏ + ๐๏ทฏ . Find the position vector of a point R which divides the line joining P and Q in the ratio 2 : 1, (i) internally, and ๐๐๏ทฏ = 3 ๐๏ทฏ โ 2 ๐๏ทฏ ๐๐๏ทฏ = ๐๏ทฏ + ๐๏ทฏ Position vector of R = 2 ๐๐๏ทฏ + 1 ๐๐๏ทฏ๏ทฎ2 + 1๏ทฏ ๐๐๏ทฏ = 2 ๐๏ทฏ + ๐๏ทฏ๏ทฏ + 1 3 ๐๏ทฏ โ 2 ๐๏ทฏ๏ทฏ๏ทฎ2 + 1๏ทฏ = 2 ๐๏ทฏ + 2 ๐๏ทฏ + 3 ๐๏ทฏ โ 2 ๐๏ทฏ๏ทฎ3๏ทฏ = ๐ ๐๏ทฏ๏ทฎ๐๏ทฏ Thus, position vector of R dividing P and Q internally is 5 ๐๏ทฏ๏ทฎ3๏ทฏ. Example 11 Consider two points P and Q with position vectors ๐๐๏ทฏ = 3 ๐๏ทฏ โ 2 ๐๏ทฏ and ๐๐๏ทฏ = ๐๏ทฏ + ๐๏ทฏ . 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 ๐๐๏ทฏ โ 1 ๐๐๏ทฏ๏ทฎ๐ โ ๐๏ทฏ ๐๐๏ทฏ = 2 ๐๏ทฏ + ๐๏ทฏ๏ทฏ โ 1(3 ๐๏ทฏ โ 2 ๐๏ทฏ)๏ทฎ2โ1๏ทฏ = 2 ๐๏ทฏ + 2 ๐๏ทฏ โ 3 ๐๏ทฏ + 2 ๐๏ทฏ๏ทฎ1๏ทฏ = โ ๐๏ทฏ + 4 ๐๏ทฏ = 4 ๐๏ทฏ โ ๐๏ทฏ Thus, position vector of R dividing P and Q externally is 4 ๐๏ทฏ โ ๐๏ทฏ

Examples