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Last updated at May 29, 2018 by Teachoo

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Supplementary Exercise Q3 Find the volumes of the following parallelepipeds whose three co –terminus edges are (i) 𝑎 = 2 𝑖 − 3 𝑗 + 4 𝑘, 𝑏 = 3 𝑖 − 𝑗 + 2 𝑘, and 𝑐 = 𝑖 + 2 𝑗 − 𝑘, Given, 𝑎 = 2 𝑖 − 3 𝑗 + 4 𝑘 , 𝑏 = 3 𝑖 – 𝑗 + 2 𝑘 , 𝑐 = 𝑖 + 2 𝑗 – 𝑘 Volume of parallelepiped = 𝒂 𝒃 𝒄 = 2−343−1212−1 = 2 −1×−1−(2×2) − (−3) 3×−1−(1×2) + 4 3×2−(1×−1) = 2 1−4+3 −3−2+4 6+1 = 2(–3) + 3 (–5) + 4(7) = –6 – 15 + 28 = 7 Supplementary Exercise Q3 Find the volumes of the following parallelepipeds whose three co –terminus edges are (ii) 𝑎 = 𝑖 − 2 𝑗 + 3 𝑘, 𝑏 = 2 𝑖 + 𝑗 − 𝑘, and 𝑐 = 2 𝑖 + 𝑗 − 𝑘, Given, 𝑎 = 𝑖 − 2 𝑗 + 3 𝑘 , 𝑏 = 2 𝑖 + 𝑗 – 𝑘 , 𝑐 = 2 𝑖 + 𝑗 – 𝑘 Volume of parallelepiped = 𝒂 𝒃 𝒄 = 1−2321−121−1 = 1 1×−1−(1×−1) − (−2) 2×−1−(2×−1) + 3 2×1−(2×1) = 1 −1+1+2 −2+2+3 2−2 = 1(0) + 2 (0) + 3(0) = 0

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 You are here

Supplementary Exercise Q4

Supplementary Exercise Q5

Supplementary Exercise Q6

Supplementary Exercise Q7

Supplementary Exercise Q8

Supplementary Exercise Q9

Supplementary Exercise Q10

About the Author

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.