Supplementary Exercise Q7 - Show that points A, B, C and D - Supplementary examples and questions from CBSE

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  1. Chapter 10 Class 12 Vector Algebra
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Supplementary Exercise Q7 Show that the four points A, B, C and D with position vectors 4 𝑖īˇ¯ + 5 𝑗īˇ¯ + 𝑘īˇ¯, −( 𝑗īˇ¯ + 𝑘īˇ¯), 3 𝑖īˇ¯ + 9 𝑗īˇ¯ + 4 𝑘īˇ¯ and −4 𝑖īˇ¯ + 4 𝑗īˇ¯ + 4 𝑘īˇ¯, respectively are co-planar 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¯ = −4īˇŽâˆ’6īˇŽâˆ’2īˇŽâˆ’1īˇŽ4īˇŽ3īˇŽâˆ’8īˇŽâˆ’1īˇŽ3īˇ¯īˇ¯ = −4 4×3īˇ¯âˆ’(−1×3) īˇ¯ − (−6) −1×3īˇ¯âˆ’(−8×3)īˇ¯ + (−2) −1×−1īˇ¯âˆ’(−8×4) īˇ¯ = –4 12+3īˇ¯+6 −3+24īˇ¯âˆ’2 1+32īˇ¯ = −4 (15) + 6 (21) − 2 (33) = −60 + 126 − 66 = −126+ 126 = 0 ∴ 𝐴đĩīˇ¯, 𝐴đļīˇ¯, 𝐴𝐷īˇ¯īˇ¯ = 0 Therefore, points A, B, C and D are coplanar.

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