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.
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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