wiz-icon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

Find λ for which the points A (3, 2, 1), B (4, λ, 5), C (4, 2, −2) and D (6, 5, −1) are coplanar.

Open in App
Solution

The points A, B, C and D will be coplanar iff any one of the following traces of vectors are coplanar:AB, AC, AD; AB, BC, CD; BC, BA, BD, etc.It is given that AB, AC, AD are coplanar.Thus, their scaler triple product AB AC AD is equal to zero.Now,Direction ratios of the PQ=Direction ratios of vector Q-Direction ratios of the vector PDirection ratios of vector AB = 4-3, λ-2, 5-1, i.e. 1, λ-2, 4Direction ratios of vector AC = 4-3, 2-2, -2-1, i.e. 1, 0, -3Direction ratios of vector AD = 6-3, 5-2,-1-1, i.e. 3, 3, -2 AB AC AD=1λ-2410-333-2=10--9-λ-2-2--9+43-0=0 7λ=35λ=5

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Extrema
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon