Supplementary Exercise Q10
Last updated at Dec. 8, 2016 by Teachoo
Transcript
Supplementary Exercise Q10 If the vectors 𝐴 = a 𝑖 + 𝑗 + 𝑘, 𝐵 = 𝑖 + b 𝑗 + 𝑘 and 𝐶 = 𝑖 + 𝑗 + c 𝑘 are coplanar, then 11−𝑎 + 11−𝑏 + 11−𝑐 = 1, where a, b, c ≠ 1 Since Vectors 𝐴, 𝐵, 𝐶 are coplanar , ∴ 𝐴 𝐵 𝐶 = 0 𝐴 𝐵 𝐶 = 𝑎111𝑏111𝑐 = 0 C1 C1 C3 C2 C2 C3 𝑎−1010𝑏−111−𝑐1−𝑐𝑐 = 0 𝑎−1010𝑏−111−𝑐1−𝑐𝑐 = 0 Expanding Determinant along C3 1 0(1 − c) − (1 − c)(b − 1) −1 (a − 1) (1 − c) − 0 + c (a − 1) (b − 1) − 0 (1 − c) (1 − b) − (a − 1) (1 − c) + c (1− a) (1 − b) = 0 (1 − c) (1 − b) + (1 − c) (1 − a) + c (1 − a) (1− b) = 0 Dividing L.H.S and R.H.S by (1 − a) (1 − b) (1 − c) 1 − 𝑐 1 − 𝑏 + 1 − 𝑐 1 − 𝑎 + 𝑐 1 − 𝑎 1 − 𝑏 1 − 𝑎 1 − 𝑏 1 −𝑐 =0 11 − 𝑎+ 11 − 𝑏+ 𝑐1 − 𝑐=0 11 − 𝑎+ 11 − 𝑏+ 𝑐1 − 𝑐=0 Adding 1 both sides 11 − 𝑎+ 11 − 𝑏+ 𝑐1 − 𝑐+1=1 11 − 𝑎+ 11−𝑏+ 𝑐 + 1 − 𝑐1 − 𝑐=1 11 − 𝑎+ 11 − 𝑏+ 11 − 𝑐=1 Hence Proved
Supplementary examples and questions from CBSE
Supplementary Example 1
Supplementary Example 2
Supplementary Example 3
Supplementary Example 4
Supplementary Example 5
Supplementary Example 6
Supplementary Exercise Q1
Supplementary Exercise Q2
Supplementary Exercise Q3
Supplementary Exercise Q4
Supplementary Exercise Q5
Supplementary Exercise Q6
Supplementary Exercise Q7
Supplementary Exercise Q8
Supplementary Exercise Q9
Supplementary Exercise Q10 You are here
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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He provides courses for Mathematics from Class 9 to 12. You can ask questions here.