Supplementary Exercise Q8
Last updated at Aug. 24, 2021 by Teachoo
Supplementary examples and questions from CBSE
Supplementary Example 2 Important Deleted for CBSE Board 2022 Exams
Supplementary Example 3 Deleted for CBSE Board 2022 Exams
Supplementary Example 4 Deleted for CBSE Board 2022 Exams
Supplementary Example 5 Important Deleted for CBSE Board 2022 Exams
Supplementary Example 6 Deleted for CBSE Board 2022 Exams
Supplementary Exercise Q1 Deleted for CBSE Board 2022 Exams
Supplementary Exercise Q2 Deleted for CBSE Board 2022 Exams
Supplementary Exercise Q3 Deleted for CBSE Board 2022 Exams
Supplementary Exercise Q4 Important Deleted for CBSE Board 2022 Exams
Supplementary Exercise Q5 Deleted for CBSE Board 2022 Exams
Supplementary Exercise Q6 Important Deleted for CBSE Board 2022 Exams
Supplementary Exercise Q7 Deleted for CBSE Board 2022 Exams
Supplementary Exercise Q8 Deleted for CBSE Board 2022 Exams You are here
Supplementary Exercise Q9 Important Deleted for CBSE Board 2022 Exams
Supplementary Exercise Q10 Deleted for CBSE Board 2022 Exams
Supplementary examples and questions from CBSE
Last updated at Aug. 24, 2021 by Teachoo
Supplementary Exercise Q8 Find the value of 𝜆 if the point A (−1, 4, −3), B = (3, 𝜆, −5), C(−3, 8, −5) and D (−3, 2, 1) are coplanar Four points A, B, C, D are coplanar if the three vectors (𝐴𝐵) ⃗ , (𝐴𝐶) ⃗ and (𝐴𝐷) ⃗ are coplanar. i.e. [(𝑨𝑩) ⃗, (𝑨𝑪) ⃗, (𝑨𝑫) ⃗ ] = 0 A (−1, 4, −3), B (3, 𝜆, −5) (𝑨𝑩) ⃗ = (3 – (-1))𝑖 ̂ + (𝜆 − 4)𝑗 ̂ + (–5 –(-3)) 𝑘 ̂ = 4𝒊 ̂ + (𝜆 − 4)𝒋 ̂ − 2𝒌 ̂ A (−1, 4, −3), C(−3, 8, −5) (𝑨𝑪) ⃗ = (-3 – (-1))𝑖 ̂ + (8 − 4)𝑗 ̂ + (–5 –(-3)) 𝑘 ̂ = –2𝒊 ̂ + 4𝒋 ̂ − 2𝒌 ̂ A (−1, 4, −3), D (−3, 2, 1) (𝑨𝑫) ⃗ = (-3 – (-1))𝑖 ̂ + (2 − 4)𝑗 ̂ + (1 –(-3)) 𝑘 ̂ = –2𝒊 ̂ – 2𝒋 ̂ + 4𝒌 ̂ [(𝐴𝐵) ⃗, (𝐴𝐶) ⃗, (𝐴𝐷) ⃗ ] = |■8(4&(𝜆−4)&−2@−2&4&−2@−2&−2&4)| 0 = 4[(4×4)−(−2×−2) ] − (𝜆 − 4) [(−2×4)−(−2×−2)] + (−2)[(−2×−2)−(−2×4) ] 0 = 4 [16−4]−"(𝜆 − 4)" [−8−4]−2[4+8] 0 = 4(12) – "(𝜆 − 4)"(–12) − 2 (12) 0 = 48 + 12"𝜆" – 48 − 24 12"𝜆" = 24 "𝜆" = 24/12 "𝜆" = 2