Plane | Equation | Coordinate |
---|---|---|
xy-plane | z = 0 | (x, y, 0) |
yz-plane | x = 0 | (0, y, z) |
zx-plane | y = 0 | (x, 0, z |
• equation of x-axis: y = 0, z = 0 • equation of y-axis: x = 0, z = 0 • equation of z-axis: x = 0, y = 0 |
PQ | = | √ (7 - 2)2 + (5 - (-3))2 + (-2 - 5)2 |
= | √ 52 + 82 + (-7)2 | |
= | √ 25 + 64 + 49 | |
= | √ 138 |
PQ | = | √ (1 - (-1))2 + (1 - 2)2 + (6 - 5)2 |
= | √ 22 + (-1)2 + 12 | |
= | √ 6 | |
QR | = | √ (0 - 1)2 + (5 - 1)2 + (6 - 6)2 |
= | √ 1 + 16 + 0 | |
= | √ 17 | |
RP | = | √ (-1 - 0)2 + (2 - 5)2 + (5 - 6)2 |
= | √ 1 + 9 + 1 | |
= | √ 11 |
(RP)2 + (PQ)2 | = | (√ 6 ) 2 + (√ 11 ) 2 |
= | 6 + 11 | |
= | 17 | |
(QR)2 | = | (√ 17 ) 2 |
= | 17 | |
∴ (QR)2 | = | (RP)2 + (PQ)2 |
AB | = | √ (3 - 1)2 + (-2 - (-1))2 + (3 - 2)2 |
= | √ 22 + (-1)2 + 12 | |
= | √ 6 | |
BC | = | √ (5 - 3)2 + (-3 - (-2))2 + (4 - 3)2 |
= | √ 22 + (-1)2 + 12 | |
= | √ 6 | |
CA | = | √ (1 - 5)2 + (-1 - (-3))2 + (2 - 4)2 |
= | √ (-4)2 + 22 + (-2)2 | |
= | √ 16 + 4 + 4 | |
= | √ 24 | |
= | √ 4 × 6 | |
= | 2 √ 6 |
AB + BC | = | √ 6 + | √ 6 |
= | 2 √ 6 |
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