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AA HL · Topic 3.13 · Vectors High frequency — Paper 1 & 2

Where this sits in the syllabus

Step 2 of 5 · 6 marks · about 6 minutes

01
Read the vectors
Identify the anchor point and the two direction lines that matter for the mark.
02
Set the angle target
Focus on the line-plane relationship and what the examiner expects to see first.
03
Write the substitution
Push the line into the plane and keep the algebra clean.
04
Solve the parameter
Get the exact point before you move back to geometry.
05
State the angle
Finish with the angle and a short exam-ready conclusion.

The line passes through A(1, 0, -2) with direction vector (2, 1, -1). The plane is x + 2y - z = 4. Use the scene to see the algebra, then write the exact intersection point.

A(1, 0, -2)
d = (2, 1, -1)
x + 2y - z = 4
6 marks

Attach Image

Lesson moment

Step 2: compare the line direction to the plane before you substitute.

What matters for the mark is seeing which expressions will replace x, y, and z when you move into algebra.

This is the exam angle you need to justify before you calculate it.

Tutor

Focus on the Angle

Keep the scene readable, anchor the reasoning to the visible vectors, and only surface the next step when it helps.

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Exam context

High frequency from Paper 1 & 2

Students usually lose marks by jumping to the angle too early, skipping the normal line, or never explaining why the final angle is the complement.

Show the normal to the plane before using any formula.
Explain the line-plane angle as the complement of the line-normal angle.
Finish with the exact angle statement the examiner can award.

Markscheme

What the examiner rewards

Marks are visible from the start so the student can work backwards from the reward structure.

M1 A1 M1 A1 R1

Ask about the marks, the method, or the mistake.

Use this tab when you want freeform help without leaving the exam flow.

AA HL Exam Tutor

Focus on the Angle

Formula

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