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Proving vectors are parallel

Show that one is a scalar multiple of the other.

  • A vector has both magnitude and direction. Reverse a route by changing its sign.
  • Use a consistent direction and match corresponding components.
  • A scalar multiple proves parallel directions. Collinearity also needs a shared point.

Example 1

The vectors a and are non-parallel. Prove that AB is parallel to CD.

Factor out the common scalar from both vector components.The same scalar multiplies the entire vector.
AB ∥ CD. This alone does not prove that A, B, C and D lie on one line.

Example 2

The vectors a and are non-parallel. Prove that AB is parallel to CD.

Factor out the common scalar from both vector components.The same scalar multiplies the entire vector.
AB ∥ CD. This alone does not prove that A, B, C and D lie on one line.

Your turn

Question 1

The vectors a and are non-parallel. Prove that AB is parallel to CD.

Check answer
Factor out the common scalar from both vector components.The same scalar multiplies the entire vector.
AB ∥ CD. This alone does not prove that A, B, C and D lie on one line.
Question 2

The vectors a and are non-parallel. Prove that AB is parallel to CD.

Check answer
Factor out the common scalar from both vector components.The same scalar multiplies the entire vector.
AB ∥ CD. This alone does not prove that A, B, C and D lie on one line.
Question 3

The vectors a and are non-parallel. Prove that AB is parallel to CD.

Check answer
Factor out the common scalar from both vector components.The same scalar multiplies the entire vector.
AB ∥ CD. This alone does not prove that A, B, C and D lie on one line.
Question 4

The vectors a and are non-parallel. Prove that AB is parallel to CD.

Check answer
Factor out the common scalar from both vector components.The same scalar multiplies the entire vector.
AB ∥ CD. This alone does not prove that A, B, C and D lie on one line.
Question 5

The vectors a and are non-parallel. Prove that AB is parallel to CD.

Check answer
Factor out the common scalar from both vector components.The same scalar multiplies the entire vector.
AB ∥ CD. This alone does not prove that A, B, C and D lie on one line.
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