Question

If [ b c d ]+[c a d ]+[a b d]=[a b c].then show that the points with position vectors a,b,c,d are complanar​

Answer 1

Answer:

⇔ vector[AB AC AD] = 0 ⇔ vector[OB - OA OC - OA OD - OA] = 0 ⇔ vector[b-a c-a d-a]= 0 ⇔ vector[b c -a d-a] - vector[a c-a d-a] = 0 ⇔ vector{[b c d-a] - [b a d-a] - [a c d-a] + [a a d-a]} = 0 ⇔ vector{[b c d] - [b c a] - [b a d] + [b a a] - [a c d]} + 0 = 0 ⇔ vector{[b c d] - [a b c] + [a b d] + 0 +[c a d]} + 0 = 0 ⇔ vector{[b c d] + [a b d] + [c a d] = [a b c]} ← Prev QuestionNext Question → Find MCQs & Mock Test Free JEE Main Mock Test Free NEET Mock Test Class 12 Chapterwise MCQ Test Class 11 Chapterwise Practice Test Class 10 Chapterwise MCQ Test Class 9 Chapterwise MCQ Test Class 8 Chapterwise MCQ Test Class 7 Chapterwise MCQ Test Related questions 0 votes 1 answer Show that three vectors a, b, c are coplanar iff vectors[a b c] = 0 asked Sep 22, 2019 in Mathematics by Deepak01 (58.7k points) jee jee mains 0 votes 1 answer If a, b, c are the position vectors of A, B, C respectively then show that A, B, C are collinear iff a× b + b×c + c× a = 0 . asked Sep 20, 2019 in Mathematics by SumanMandal (54.6k points) jee mains jee 0 votes 1 answer Let R be a relation in the set of integer I defined by aRb iff a & b both are neither even nor odd. Then show that R is asked Feb 6, 2020 in Mathematics by KumariMuskan (33.9k points) bseb model set class-12 0 votes 1 answer Show that two lines with slopes m1 and m2 are (i) parallel iff m1 = m2 asked Feb 2, 2020 in Mathematics by Sarita01 (53.5k points) straight lines class-11 0 votes 1 answer Show that a, b, c are in A.P. iff 3tanA/2.tanC/2 = 1 asked Sep 19, 2019 in Mathematics by SumanMandal (54.6k points) jee jee mains Read more on Sarthaks.com - https://www.sarthaks.com/490080/show-that-the-four-points-vectors-a-b-c-d-are-coplanar-iff-b-c-d-c-a-d-a-b-d-a-b-c