Check sibling questions

Slide38.JPG

Slide39.JPG

Learn in your speed, with individual attention - Teachoo Maths 1-on-1 Class


Transcript

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

Ask a doubt
Davneet Singh's photo - Co-founder, Teachoo

Made by

Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.