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Question

Consider three planes:
2x+py+6z=8x+2y+qz=5x+y+3z=4
The three planes intersect at a point if 


Your Answer
A
p=2,q3
Correct Answer
B
p2,q3
 
Your Answer
C
p2,q=3
 
Your Answer
D
p=2,q=3

Solution

The correct option is A p2,q3
 
Given planes are:

2x+py+6z=8x+2y+qz=5x+y+3z=4

Augmented matrix, A=2p6812q51134

We will find the rank of matrix A. For the planes to intersect in a point, the rank of this matrix must be 3.

R3R312R1 and R2R212R1

A=⎢ ⎢2p6802p2q3101p200⎥ ⎥

For the given system of equation to have unique solution,
1p20 and q30
p2 and q3

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