Examples
Example 2 Important
Example 3 Important
Example 4
Example 5
Example 6 Important
Example 7
Example 8 Important
Example 9
Example 10
Example 11 (i) Important
Example 11 (ii) Important
Example 12 Important
Example 13
Example 14 Important
Example 15
Example 16 Important
Example 17
Example 18 Important
Example 19
Example 20
Example 21 Important
Example 22
Example 23 Important
Example 24
Example 25 Important
Example 26
Example 27 Important
Example 28 Important
Example 29 Important
Example 30 Important
Example 26 (Supplementary NCERT) Deleted for CBSE Board 2025 Exams
Example 27 (Supplementary NCERT) Deleted for CBSE Board 2025 Exams You are here
Example 28 (Supplementary NCERT) Important Deleted for CBSE Board 2025 Exams
Example 29 (Supplementary NCERT) Important Deleted for CBSE Board 2025 Exams
Example 30 (Supplementary NCERT) Important Deleted for CBSE Board 2025 Exams
Example 31 (Supplementary NCERT) Important Deleted for CBSE Board 2025 Exams
Last updated at April 16, 2024 by Teachoo
Example 27 (Supplementary NCERT) Show that the vectors 𝑎 ⃗ = 𝑖 ̂ − 2𝑗 ̂ + 3𝑘 ̂, 𝑏 ⃗ = −2𝑖 ̂ + 3𝑗 ̂ − 4𝑘 ̂ and 𝑐 ⃗ = 𝑖 ̂ − 3𝑗 ̂ + 5𝑘 ̂ are coplanarThree vectors 𝑎 ⃗, 𝑏 ⃗, 𝑐 ⃗ are coplanar if [𝒂 ⃗" " 𝒃 ⃗" " 𝒄 ⃗ ] = 0 Given, 𝒂 ⃗ = 𝑖 ̂ − 2𝑗 ̂ + 3𝑘 ̂ 𝒃 ⃗ = −2𝑖 ̂ + 3𝑗 ̂ − 4𝑘 ̂ 𝒄 ⃗ = 𝑖 ̂ − 3𝑗 ̂ + λ𝑘 ̂ [𝒂 ⃗" " 𝒃 ⃗" " 𝒄 ⃗ ] = |■8(1&−2&3@−2&3&−4@1&−3&5)| = 1[(3×5)−(−3×−4) ] − (−2) [(−2×5)−(1×−4) ] + 3[(−2×−3)−(1×3) ] = 1 [15−(3 ×4)]+2[−10−(−4)]+3[(2 ×3)−3] = 1 [15−12]+2[−10+4]+3[6−3] = 1 [3]+2[−6]+3[3] = 3 – 12 + 9 = 0 Since [𝑎 ⃗" " 𝑏 ⃗" " 𝑐 ⃗ ] = 0 Vectors 𝒂 ⃗, 𝒃 ⃗, 𝒄 ⃗ are coplanar