Vectors and matrices — Question 9

QCAA 2023, Paper 1 · 1 mark

Q9 · 2023 · Technology-freeSimple familiar1 mark

QUESTION 9

The geometric interpretation of a certain system of three equations with no solution is shown. Given two of the equations are

x+y-z=0.5

and

x-y-z=0.5

, the third equation could be

Geometric interpretation of three planes with no common solution.

(A)

2x-2y-2z=1

(B)

2x+2y-2z=1

(C)

2x-2y+2z=3

(D)

2x+2y-2z=3

ABCD

Question linkOriginal paper

WORKED SOLUTION

Answer D

1 mark

ANSWER

Worked solution

Doubling the first equation gives

2x+2y-2z=1

. Option D has the same left-hand side but a different right-hand side, so it represents a distinct plane parallel to the first. Therefore the three-plane system has no common solution, matching the diagram.

Selects option D.

[1 mark]

Worked explanation by QCE Vault; correct option verified against the QCAA answer key.

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