Te collinear. je and + 2* à =
fedlem: If the points whose position vectors are 3 i - 2j-k. 2 i + 37 - 4k
*4 + 5j + k are coplanar, then show that =
Let the given points be A, B, C and Drespectively.
Then AB =-i + 5j-3k, AC =-4i+3j + 3k and
17
AD = i +7+ ( + 1)
& Cand D are coplanarif and only if
AD = r AB + y AC, for some scalarse y that is
5+& = x(-i +3j - 3k ) + y(-4i +3j + 38)
Equating the corresponding coefficients
- r- 4y = 1, 5r + 3y = 7. - 3x + 3y = A +1
31 12
Solving the first two equations we get :=
17 17
146
nd hence = - 3x + 3y - 1 = -
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