Ex 10.2, 13 - Chapter 10 Class 12 Vector Algebra
Last updated at Dec. 16, 2024 by Teachoo
Last updated at Dec. 16, 2024 by Teachoo
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 ̂ = –2𝑖 ̂ – 4𝑗 ̂ + 4𝑘 ̂ 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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