Ex 10.2, 16 - Find position vector of mid point of vector - Section formula

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

Transcript

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, โ€“2). P(2,3,4) , Q(4, 1, โˆ’2) Let the midpoint of PQ be R. Position vector of P = (2 โˆ’ 0) ๐‘–๏ทฏ + (3 โˆ’ 0) ๐‘—๏ทฏ + (4 โˆ’ 0) ๐‘˜๏ทฏ ๐‘‚๐‘ƒ๏ทฏ = 2 ๐‘–๏ทฏ + 3 ๐‘—๏ทฏ + 4 ๐‘˜๏ทฏ Position vector of Q = (4 โˆ’ 0) ๐‘–๏ทฏ + (1 โˆ’ 0) ๐‘—๏ทฏ + (โˆ’2 โˆ’ 0) ๐‘˜๏ทฏ ๐‘‚๐‘„๏ทฏ = 4 ๐‘–๏ทฏ + 1 ๐‘—๏ทฏ โˆ’ 2 ๐‘˜๏ทฏ Position vector of R = ๐‘ถ๐‘ธ๏ทฏ + ๐‘ถ๐‘ท๏ทฏ๏ทฎ๐Ÿ๏ทฏ ๐‘‚๐‘…๏ทฏ = 4 ๐‘–๏ทฏ + 1 ๐‘—๏ทฏ โˆ’ 2 ๐‘˜๏ทฏ๏ทฏ + (2 ๐‘–๏ทฏ + 3 ๐‘—๏ทฏ + 4 ๐‘˜๏ทฏ)๏ทฎ2๏ทฏ ๐‘‚๐‘…๏ทฏ = 4 + 2๏ทฏ ๐‘–๏ทฏ + 1 + 3๏ทฏ ๐‘—๏ทฏ + (โˆ’2 + 4) ๐‘˜๏ทฏ๏ทฎ2๏ทฏ ๐‘‚๐‘…๏ทฏ = 6 ๐‘–๏ทฏ + 4 ๐‘—๏ทฏ + 2 ๐‘˜๏ทฏ๏ทฎ2๏ทฏ ๐‘‚๐‘…๏ทฏ = 2(3 ๐‘–๏ทฏ + 2 ๐‘—๏ทฏ + ๐‘˜๏ทฏ)๏ทฎ2๏ทฏ ๐‘‚๐‘…๏ทฏ = ๐Ÿ‘ ๐’Š๏ทฏ+๐Ÿ ๐’‹๏ทฏ+ ๐’Œ๏ทฏ Therefore, position vector of midpoint of PQ is 3 ๐‘–๏ทฏ + 2 ๐‘—๏ทฏ + ๐‘˜๏ทฏ

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