Question

a. Determine if u = [2, 7, −1], v = [5, −3, 2] and w = [9, 11, 2] are coplanar.
(show steps please)

b. Please explain why it is/isn't coplanar.

Answer 1

to prove that three vectors u,v,w to be coplanar, express one of these vectors as the linear combination of the other two i.e write w = x u + y v

given :
u = [2, 7, −1], v = [5, −3, 2] and w = [9, 11, 2]

let the vector w can represented as :
w = 2u + v
proving :
w = 2[2, 7, −1] + [5, −3, 2]
w = [4, 14, -2] + [5, −3, 2]
w = [9, 11, 0]

nah, the third component of vector w not same like given above. so it is not coplanar

Answer 2

Thank you :)

Answer 3

does that make sense ?

Answer 4

Yes, I just needed the straight answer, that cleared it up :)

Answer 5

youre welcome ;)