Supplementary Example 2

Transcript

Supplementary Example 2 Find the volume of the parallelepiped whose edges are 𝑎﷯ = 2 𝑖﷯ − 3 𝑗﷯ + 4 𝑘﷯, 𝑏﷯ = 𝑖﷯ + 2 𝑗﷯ − 𝑘﷯ and 𝑐﷯ = 2 𝑖﷯ − 𝑗﷯ + 2 𝑘﷯ Given, 𝑎﷯ = 2 𝑖﷯ − 3 𝑗﷯ + 4 𝑘﷯ , 𝑏﷯ = 𝑖﷯ + 2 𝑗﷯ – 𝑘﷯ , 𝑐﷯ = 2 𝑖﷯ – 𝑗﷯ + 2 𝑘﷯ Volume of parallelepiped = 𝒂﷯ 𝒃﷯ 𝒄﷯﷯ = 2﷮−3﷮4﷮1﷮2﷮−1﷮2﷮−1﷮2﷯﷯ = 2 2×2﷯−(−1×−1) ﷯ − (−3) 1×2﷯−(2×−1) ﷯ + 4 1×−1﷯−(2×2)﷯ = 2 4−1﷯+3 2+2﷯+4 −1−4﷯ = 2(3) + 3 (4) + 4(–5) = 6 + 12 – 20 = –2 Since volume is always positive Volume of parallelepiped = 2 cubic units