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Supplementary Exercise Q8 - Find value of if points A, B, C, D - Supplementary examples and questions from CBSE

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  1. Chapter 10 Class 12 Vector Algebra
  2. Serial order wise
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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 𝐴đĩīˇ¯ , 𝐴đļīˇ¯ and 𝐴𝐷īˇ¯ are coplanar. i.e. 𝑨𝑩īˇ¯, 𝑨đ‘Ēīˇ¯, 𝑨đ‘Ģīˇ¯īˇ¯ = 0 𝐴đĩīˇ¯, 𝐴đļīˇ¯, 𝐴𝐷īˇ¯īˇ¯ = 4īˇŽ(𝜆−4)īˇŽâˆ’2īˇŽâˆ’2īˇŽ4īˇŽâˆ’2īˇŽâˆ’2īˇŽâˆ’2īˇŽ4īˇ¯īˇ¯ 0 = 4 4×4īˇ¯âˆ’(−2×−2) īˇ¯ − (𝜆 − 4) −2×4īˇ¯âˆ’(−2×−2)īˇ¯ + (−2) −2×−2īˇ¯âˆ’(−2×4) īˇ¯ 0 = 4 16−4īˇ¯âˆ’(𝜆 − 4) −8−4īˇ¯âˆ’2 4+8īˇ¯ 0 = 4(12) – (𝜆 − 4)(–12) − 2 (12) 0 = 48 + 12𝜆 – 48 − 24 12𝜆 = 24 𝜆 = 24īˇŽ12īˇ¯ 𝜆 = 2

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