QCE Vault / Specialist Maths Vectors in three dimensions — Question 35 Original QCE Vault practice · 1 mark
Browse all questions Vectors revision Original practice exam Report an issue Q35 · Practice question Simple familiar 1 mark
QUESTION 35 The line r = ( 0 , 0 , 1 ) + t ( 1 , 2 , − 1 ) \mathbf r=(0,0,1)+t(1,2,-1) r = ( 0 , 0 , 1 ) + t ( 1 , 2 , − 1 ) and the plane 2 x − y = 3 2x-y=3 2 x − y = 3 are (C) intersecting at one point
(D) such that the line lies in the plane
WORKED SOLUTION
Answer B 1 mark Worked solution
The direction vector ( 1 , 2 , − 1 ) (1,2,-1) ( 1 , 2 , − 1 ) has scalar product zero with the plane normal ( 2 , − 1 , 0 ) (2,-1,0) ( 2 , − 1 , 0 ) . The point ( 0 , 0 , 1 ) (0,0,1) ( 0 , 0 , 1 ) is not on the plane, so the line and plane are parallel and distinct. Selects the correct option.
[1 mark] Practice question aligned to the current QCAA syllabus; review the worked solution and marking criteria.
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