The vector equation of plane is given as,
r=(1−x−y)a+xb+yc If a, b, c, d are coplanar, then d satisfy for some x, y.
d=(1−x−y)a+xb+yc …… (1)
From the given data,
6d=2a−3b+7c 6d= Substitute the value in equation (1),
=(1−x−y)a+xb+yc 1−x−y= …… (2)
Solve equation (1) and equation (2),
x=− and
y= Substitute the values in equation (2),
1−(−)−= The values of x and y satisfy equation (2),
Thus, b lie on plane.
Therefore, A is correct, R is correct and R is correct explanation for A.