Determine beta and alpha by using vectors such that A, B and C lie in the same plane, given that vector vec(AB)=−4vec(i)−vec(j) −2vec(k) and vector vec(BC)=4 vec(i) +(beta+3)vec(j) +(alpha−6)vec(k)

Nica2t 2022-08-13 Answered
Determine β and α by using vectors such that A, B and C lie in the same plane, given that vector A B = 4 ı ȷ 2 k and vector B C = 4 ı + ( β + 3 ) ȷ + ( α 6 ) k
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Answers (1)

optativaspv
Answered 2022-08-14 Author has 14 answers
Any three points in 3D space will inevitably be on the same plane.
To show this, you can take:
a = A B
b = B C
c = A C = A B + B C
and you will get that a ( b × c ) = 0, regardless of α and β
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