TS EAMCET 5 May 2018 Shift 1 Solved Paper

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=

2a−3b+7c

6

Substitute the value in equation (1),

2a−3b+7c

6

=(1−x−y)a+xb+yc
1−x−y=

1

3

…… (2)
Solve equation (1) and equation (2),
x=−

1

2

and y=

7

6

Substitute the values in equation (2),
1−(−

1

2

)−

7

6

=

1

3

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.