Calculus & Vectors (MCV4U) · Lines Planes 3D

Intersections of Lines and Planes, and Planes and Planes

10 tutor-authored questions for this Ontario curriculum expectation, ordered easiest to hardest — every one with a full worked solution. Work through them free, no account needed.

Start the 10 questions Curriculum: MCV4U-LP3.4

Sample: the first question, solved

A line's parametric equations satisfy a plane's equation for every value of t. What does this mean?

📘 Worked solution
If substituting the line into the plane's equation gives a true statement for all t, every point on the line satisfies the plane's equation, so the line lies entirely in the plane.

And one from the hard end

Is the line r=(1,0,0)+t(0,1,0) parallel to the plane 2x+3y−z=5?

Solution shown after you try it in practice mode.

Work through all 10, easiest to hardest

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