Grade 12 Vectors Worksheets
Free printable vectors practice for Grade 12 students. Generate problems, solve them on screen or paper, and download as PDF.
What your child will practice
- Vectors in 2D and 3DRepresent vectors geometrically and algebraically in two and three dimensions.
- Dot ProductCalculate and interpret the dot product of two vectors.
- Cross ProductCalculate and interpret the cross product of two vectors in 3D.
- Equations of PlanesRepresent planes in 3D using scalar, vector, and parametric equations.
- Intersections of Lines and PlanesDetermine intersections of lines with lines, lines with planes, and planes with planes.
Free Practice Worksheets
Print, solve on paper, then upload a photo for instant AI grading and feedback.
Build confidence with approachable problems
Solve each problem. Take your time.
- 1.Given vector u = (3, -1) and vector v = (2, 5), find the resultant vector u + v.
- 2.Given vector a = (5, 2) and vector b = (1, 4), find the resultant vector a - b.
- 3.Given vector c = (2, 3) and scalar k = 4, find the scalar multiple 3c.
- 4.Given vector p = (1, 0, 2) and vector q = (3, -1, 4), find the resultant vector p + q.
- 5.Given vector r = (6, -2, 0) and vector s = (1, 3, -5), find the resultant vector r - s.
- 6.Given vector t = (-2, 1, 3) and scalar m = -2, find the scalar multiple -2t.
Full range of grade expectations
Solve each problem. Show your work.
- 1.Given vectors u = <3, -1, 2> and v = <-2, 4, 1>, find the following: a) u + v b) 3u - 2v c) The magnitude of u, ||u||
- 2.Two forces are acting on an object. Force F1 is represented by the vector <5, -3> Newtons and Force F2 is represented by the vector <-2, 7> Newtons. Calculate the resultant force vector and its magnitude.
- 3.Find the dot product of vectors a = <2, 5> and b = <-3, 1>. Are these vectors orthogonal? Explain why or why not.
- 4.Calculate the cross product of vectors p = <1, 0, -2> and q = <3, 2, 1>. Verify that the resulting vector is orthogonal to both p and q.
- 5.A small airplane is flying with an airspeed of 200 km/h on a heading of 060 degrees. There is a wind blowing from the west at 40 km/h. Determine the resultant velocity vector of the airplane relative to the ground, and find its speed and direction.
- 6.Find the parametric equations for the line passing through the point (1, -2, 3) and parallel to the vector <4, 5, -6>.
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Create a Free AccountFrequently Asked Questions
How often should my child practice vectors?
Short daily practice sessions of 10-15 minutes are more effective than long weekly sessions. Consistency builds lasting understanding.
How do I know if my child is at the right level for these worksheets?
If your child can complete about 70% of the problems correctly, the level is appropriate. If it's too easy or too hard, try an adjacent grade level.
Can I use these worksheets for homeschool?
Yes. The worksheets align with standard curriculum expectations and can supplement any math program. Generate multiple worksheets to create a full practice set.