This question is the same as Example 27 (Supplementary NCERT)
Last updated at May 6, 2021 by Teachoo
Transcript
Ex 10.5, 2 (Supplementary NCERT) Show that the vectors ๐ โ = ๐ ฬ โ 2๐ ฬ + 3๐ ฬ, ๐ โ = โ2๐ ฬ + 3๐ ฬ โ 4๐ ฬ and ๐ โ = ๐ ฬ โ 3๐ ฬ + 5๐ ฬ are coplanarThree vectors ๐ โ, ๐ โ, ๐ โ are coplanar if [๐ โ" " ๐ โ" " ๐ โ ] = 0 Given, ๐ โ = ๐ ฬ โ 2๐ ฬ + 3๐ ฬ ๐ โ = โ2๐ ฬ + 3๐ ฬ โ 4๐ ฬ ๐ โ = ๐ ฬ โ 3๐ ฬ + ฮป๐ ฬ Now, [๐ โ" " ๐ โ" " ๐ โ ] = |โ 8(1&โ2&3@โ2&3&โ4@1&โ3&5)| = 1[(3ร5)โ(โ3รโ4) ] โ (โ2) [(โ2ร5)โ(1รโ4) ] + 3[(โ2รโ3)โ(1ร3) ] = 1 [15โ(3 ร4)]+2[โ10โ(โ4)]+3[(2 ร3)โ3] = 1 [15โ12]+2[โ10+4]+3[6โ3] = 1 [3]+2[โ6]+3[3] = 3 โ 12 + 9 = 0 Since [๐ โ" " ๐ โ" " ๐ โ ] = 0 Vectors ๐ โ, ๐ โ, ๐ โ are coplanar
Ex 10.5 (Supplementary NCERT)
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Ex 10.5 (Supplementary NCERT)
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