Calculus & Vectors (MCV4U) · Geometry and Algebra of Vectors

Vector equation of a line and intersection of two lines

Write the parametric equation of a line through two points, evaluate a point on it, or find where two lines intersect. Unlimited questions, five difficulty levels, and a full worked solution every time — free.

Practice this skill Curriculum: MCV4U-GV3.1, MCV4U-GV4.1

Try one

A line has vector equation (x, y) = (-1, 2) + t(1, -4). Find the point on the line when t = -2.

  • (−2, 11)
  • (1, −6)
  • (−3, 10)
  • (3, −8)

Answer: (-3, 10)

See one solved, step by step

A line passes through A = (6, -4, -2) and B = (9, -5, -3). Find its direction vector.

  • (−3, 1, 1)
  • (15, −9, −5)
  • (9, −5, −3)
  • (3, −1, −1)
📘 Worked solution
1Direction vector = B - A = (9, −5, −3) - (6, −4, −2) = (3, −1, −1)Subtract the corresponding coordinates of A from B to get a vector pointing along the line.

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