Check sibling questions

Ex 10.5, 4 (Supplementary NCERT) - Let a = i + j + k, b = i and c = c1

Ex 10.5, 4 (Supplementary NCERT) - Chapter 10 Class 12 Vector Algebra - Part 2

Ex 10.5, 4 (Supplementary NCERT) - Chapter 10 Class 12 Vector Algebra - Part 3

Ex 10.5, 4 (Supplementary NCERT) - Chapter 10 Class 12 Vector Algebra - Part 4


Transcript

Ex 10.5, 4 (Supplementary NCERT) Let π‘Ž βƒ— = 𝑖 Μ‚ + 𝑗 Μ‚ + π‘˜ Μ‚, 𝑏 βƒ— = 𝑖 Μ‚ and 𝑐 βƒ— = c1𝑖 Μ‚ + c2𝑗 Μ‚ + c3π‘˜ Μ‚ are coplanar (a) If c1 = 1 and c2 = 2, find c3 which makes π‘Ž βƒ—, 𝑏 βƒ—, 𝑐 βƒ— coplanar Given c1 = 1 and c2 = 2 So, our vectors become 𝒂 βƒ— = π’Š Μ‚ + 𝒋 Μ‚ + π’Œ Μ‚ 𝒃 βƒ— = 𝑖 Μ‚ 𝒄 βƒ— = c1𝑖 Μ‚ + c2𝑗 Μ‚ + c3π‘˜ Μ‚ Three vectors π‘Ž βƒ—, 𝑏 βƒ—, 𝑐 βƒ— are coplanar if [𝒂 βƒ—" " 𝒃 βƒ—" " 𝒄 βƒ— ] = 0 Ex 10.5, 4 (Supplementary NCERT) Let π‘Ž βƒ— = 𝑖 Μ‚ + 𝑗 Μ‚ + π‘˜ Μ‚, 𝑏 βƒ— = 𝑖 Μ‚ and 𝑐 βƒ— = c1𝑖 Μ‚ + c2𝑗 Μ‚ + c3π‘˜ Μ‚ are coplanar (b) If c2 = –1 and c3 = 1, show that no value of c1 can make π‘Ž βƒ—, 𝑏 βƒ—, 𝑐 βƒ— coplanar Given c2 = –1 and c3 = 1 So, our vectors 𝒂 βƒ— = 𝑖 Μ‚ + 𝑗 Μ‚ + π‘˜ Μ‚ 𝒃 βƒ— = 𝑖 Μ‚ 𝒄 βƒ— = c1𝑖 Μ‚ + c2𝑗 Μ‚ + c3π‘˜ Μ‚ Three vectors π‘Ž βƒ—, 𝑏 βƒ—, 𝑐 βƒ— are coplanar if [𝒂 βƒ—" " 𝒃 βƒ—" " 𝒄 βƒ— ] = 0 Finding [𝒂 βƒ—" " 𝒃 βƒ—" " 𝒄 βƒ— ] [π‘Ž βƒ—" " 𝑏 βƒ—" " 𝑐 βƒ— ] = |β– 8(1&1&1@1&0&0@𝑐_1&βˆ’1&1)| = 1[(0Γ—1)βˆ’(0Γ—βˆ’1) ] βˆ’ 1[(1Γ—1)βˆ’(𝑐_1Γ—0) ] + 1[(1Γ—βˆ’1)βˆ’(𝑐_1Γ—0) ] = 1 [0βˆ’0]βˆ’1[1βˆ’0]+1[βˆ’1βˆ’0] = 0 – 1 – 1 = –2 Thus, [𝒂 βƒ—" " 𝒃 βƒ—" " 𝒄 βƒ— ] β‰  0 for any value of c1 So, we can write that π‘Ž βƒ—,𝑏 βƒ—,𝑐 βƒ— are not coplanar for any value of c1

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Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths and Science at Teachoo.