Ex 10.2, 13 - Find direction cosines of A (1, 2, -3), B(-1, -2, 1) - Joining two points

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Ex 10.2, 13 Find the direction cosines of the vector joining the points A (1, 2,−3) and B(−1,−2,1), directed from A to B. A( 1, 2 , −3) B(−1, −2, 1) 𝐴𝐵﷯ = (−1 − 1) 𝑖﷯ + (−2 − 2) 𝑗﷯ + (1−(−3)) 𝑘﷯ = –2 𝑖﷯ – 4 𝑗﷯ + 4 𝑘﷯ Directions ratios are a = – 2, b = –4, & c = 4 Magnitude of 𝐴𝐵﷯ = ﷮ −2﷯﷮2﷯+ −4﷯﷮2﷯+42﷯ 𝐴𝐵﷯﷯ = ﷮4+16+16﷯ = ﷮36﷯ = 6 Directions cosines are 𝑎﷮ 𝐴𝐵﷯﷯﷯, 𝑏﷮ 𝐴𝐵﷯﷯﷯, 𝑐﷮ 𝐴𝐵﷯﷯﷯﷯ = −2﷮6﷯, −4﷮6﷯, 4﷮6﷯﷯ = −𝟏﷮𝟑﷯, −𝟐﷮𝟑﷯, 𝟐﷮𝟑﷯﷯

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