Ex 10.2

Ex 10.2, 1

Ex 10.2, 2

Ex 10.2, 3 Important

Ex 10.2, 4

Ex 10.2, 5 Important

Ex 10.2, 6

Ex 10.2, 7 Important

Ex 10.2, 8

Ex 10.2, 9

Ex 10.2, 10 Important

Ex 10.2, 11 Important You are here

Ex 10.2, 12

Ex 10.2, 13 Important

Ex 10.2, 14

Ex 10.2, 15 Important

Ex 10.2, 16

Ex 10.2, 17 Important

Ex 10.2, 18 (MCQ) Important

Ex 10.2, 19 (MCQ) Important

Last updated at April 16, 2024 by Teachoo

Ex 10.2, 11 (Method 1) Show that the vectors 2𝑖 ̂ − 3𝑗 ̂ + 4𝑘 ̂ and − 4𝑖 ̂ + 6 𝑗 ̂ − 8𝑘 ̂ are collinear.Two vectors are collinear if they are parallel to the same line. Let 𝑎 ⃗ = 2𝑖 ̂ − 3𝑗 ̂ + 4𝑘 ̂ and 𝑏 ⃗ = –4𝑖 ̂ + 6𝑗 ̂ – 8𝑘 ̂ Magnitude of 𝑎 ⃗ = √(22+(−3)2+42) |𝑎 ⃗ | = √(4+9+16) = √29 Directions cosines of 𝑎 ⃗ = (2/√29,(−3)/√29,4/√29) Magnitude of 𝑏 ⃗ =√((−4)2+62+(−8)2) |𝑏 ⃗ | = √(16+36+64) = √116 = 2√29 Directions cosines of 𝑏 ⃗ = ((−4)/(2√29),6/(2√29),(−8)/(2√29)) = ((−2)/√29,3/√29,(−4)/√29) = −1(2/√29,(−3)/√29,4/√29) Hence, Direction cosines of 𝒂 ⃗ = (−1) × Direction cosines of 𝒃 ⃗ ∴ They have opposite directions Since 𝑎 ⃗ and 𝑏 ⃗ are parallel to the same line 𝑚 ⃗, they are collinear. Hence proved Ex 10.2, 11 (Method 2) Show that the vectors 2𝑖 ̂ − 3𝑗 ̂ + 4𝑘 ̂ and − 4𝑖 ̂ + 6 𝑗 ̂ − 8𝑘 ̂ are collinear.𝑎 ⃗ = 2𝑖 ̂ − 3𝑗 ̂ + 4𝑘 ̂ 𝑏 ⃗ = –4𝑖 ̂ + 6𝑗 ̂ – 8𝑘 ̂ Two vectors are collinear if their directions ratios are proportional 𝑎_1/𝑏_1 = 𝑎_2/𝑏_2 = 𝑏_3/𝑏_3 = 𝜆 2/(−4) = (−3)/6 = 4/(−8) = (−1)/2 Since, directions ratios are proportional Hence, 𝑎 ⃗ & 𝑏 ⃗ are collinear