Question 175 of 379MediumMCQ
The sum of all values of α for which the points with position vectors i^−2j^+3k^, 2i^−3j^+4k^, (α+1)i^+2k^, 9i^+(α−8)j^+6k^ are coplanar is: Solutions · 1
Official solution
With A=(1,−2,3), B=(2,−3,4), C=(α+1,0,2), D=(9,α−8,6):
AB=(1,−1,1), AC=(α,2,−1), AD=(8,α−6,3).
\[\begin{vmatrix}1&-1&1\\ \alpha&2&-1\\8&\alpha-6&3\end{vmatrix}=0 \implies \alpha^2-2\alpha-8=0 \implies \alpha=4,-2\]
Sum =4+(−2)=2. Answer the question to unlock