Calculus & Vectors (MCV4U) · Lines Planes 3D

Intersections of Lines and Planes, and Planes and Planes

30 tutor-authored questions for this Ontario curriculum expectation, ordered easiest to hardest, every one with a full worked solution. Work through all 30 with your weekly-lesson access code.

Start the 30 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

"Find the line of intersection of x+2y−z=4 and x−y+2z=1."

Solution shown after you try it in practice mode.

Work through all 30, easiest to hardest

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