Supplementary Exercise Q8
Last updated at Aug. 24, 2021 by Teachoo
Last updated at Aug. 24, 2021 by Teachoo
Transcript
Supplementary Exercise Q8 Find the value of ๐ if the point A (โ1, 4, โ3), B = (3, ๐, โ5), C(โ3, 8, โ5) and D (โ3, 2, 1) are coplanar Four points A, B, C, D are coplanar if the three vectors (๐ด๐ต) โ , (๐ด๐ถ) โ and (๐ด๐ท) โ are coplanar. i.e. [(๐จ๐ฉ) โ, (๐จ๐ช) โ, (๐จ๐ซ) โ ] = 0 A (โ1, 4, โ3), B (3, ๐, โ5) (๐จ๐ฉ) โ = (3 โ (-1))๐ ฬ + (๐ โ 4)๐ ฬ + (โ5 โ(-3)) ๐ ฬ = 4๐ ฬ + (๐ โ 4)๐ ฬ โ 2๐ ฬ A (โ1, 4, โ3), C(โ3, 8, โ5) (๐จ๐ช) โ = (-3 โ (-1))๐ ฬ + (8 โ 4)๐ ฬ + (โ5 โ(-3)) ๐ ฬ = โ2๐ ฬ + 4๐ ฬ โ 2๐ ฬ A (โ1, 4, โ3), D (โ3, 2, 1) (๐จ๐ซ) โ = (-3 โ (-1))๐ ฬ + (2 โ 4)๐ ฬ + (1 โ(-3)) ๐ ฬ = โ2๐ ฬ โ 2๐ ฬ + 4๐ ฬ [(๐ด๐ต) โ, (๐ด๐ถ) โ, (๐ด๐ท) โ ] = |โ 8(4&(๐โ4)&โ2@โ2&4&โ2@โ2&โ2&4)| 0 = 4[(4ร4)โ(โ2รโ2) ] โ (๐ โ 4) [(โ2ร4)โ(โ2รโ2)] + (โ2)[(โ2รโ2)โ(โ2ร4) ] 0 = 4 [16โ4]โ"(๐ โ 4)" [โ8โ4]โ2[4+8] 0 = 4(12) โ "(๐ โ 4)"(โ12) โ 2 (12) 0 = 48 + 12"๐" โ 48 โ 24 12"๐" = 24 "๐" = 24/12 "๐" = 2
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