Collinear vectors

In the picture

1. 1The shared starting point of both arrows: the common origin.
2. 2The short arrow to the second dot: a vector along the straight line.
3. 3The long arrow to the third dot: twice the length in the same direction.
4. 4The short arrow on the parallel line pointing the other way: a negative multiple.

Examples

• A car driving east and another car driving east twice as fast: their velocity vectors are collinear.
• Two ropes pulling in opposite directions along the same straight line.

Quiz: Collinear vectors (Age 15)

1. 1

   When are two vectors collinear?

   • When they have exactly the same length.
   • When they start at the same point.
   • When one is a scalar multiple of the other.
2. 2

   If vector b is a negative multiple of vector a, what is true about a and b?

   • They are collinear and point in the same direction.
   • They are collinear and point in opposite directions.
   • They are not collinear.
3. 3

   What does collinearity mean for the points or lines of two vectors?

   • Their points lie on one straight line, or the lines carrying them are parallel.
   • Their points always form a triangle.
   • Their lines always meet at exactly one point.

The answers, each with its explanation, are in the app. This lesson has left the free week, so its quiz is part of the subscription.