Question

the value of x when the points A(2,-1,1), B(4,0,3), C(x,1,1) and D(2,4,3) are coplaner is​

Answer 1

Given

A(2,-1,1), B(4,0,3), C(x,1,1) and D(2,4,3) are coplaner

 To Find

 The value of X

   Solution

   A  (2,−1,1)

   B  (4,0,3)

   C  (x,1,1)

   D (2,4,3)

  AB  vector  = (2,1,2)

 AC  vector = (X−2,2,0)

 AD  vector = (0,5,2)          

 $\left[\begin{array}{ccc}2&1&2\\x-2&2&0\\0&5&2\end{array}\right]$   =  0

2(4) - 1 (2x-4) + 2 (5x-10) = 0

8 - 2x + 4 + 10x - 20 = 0

8x = 8

∴ x = 1

Hence, the value of x is 1