SpatialMath.ai - AA HL Exam Tutor

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 substitution path
Match the moving point on the line to the plane equation before you solve anything.
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 intersection
Finish with the exact point in coordinates and one clean exam-ready sentence.

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

Here is the line and the plane. Rotate the scene and notice where the line is heading before you substitute.

The mark comes from turning the moving point on the line into x, y, and z values that satisfy the plane equation.

This is the contact point the examiner wants you to justify.

Tutor

Track the contact point

Keep the scene readable, then turn the picture into one clean substitution and one exact point.

Guided Live

Exam context

High frequency from Paper 1 & 2

Students usually lose marks by substituting too fast, solving the parameter incorrectly, or never stating the exact coordinates clearly.

Write the line parametrically before you substitute.
Keep the one-variable equation in the parameter clean and readable.
Finish with the exact intersection point 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 A1 R1 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

Track the contact point

Formula

Full solution