If four points A, B, C and D with position vectors 
and 
respectively are coplanar, then find the value of x.
Formula: -
(iii) Three vectors a⃗ ,b⃗ , and c⃗ are coplanar if and only if a⃗.(b⃗×c⃗) = 0
let position vector of
position vector of
position vector of
position vector of
The four points are coplanar if the vector 
are coplanar
⇒ 1(9) – (x – 2)( – 2 + 9) + 4(3) = 0
⇒ 9 – 7x + 14 + 12 = 0
⇒ 35 = 7x
⇒ x = 5
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