Question

Prove that two non-zero vectors are collinear if and only if one vector is a scalar multiple of the other.

Answer 1

The Prove that two non-zero vectors are collinear if and only if one vector is a scalar multiple of the other is given below.

What are the proves?

1.  To know  collinear vectors:

∧ ⁻a ║ ⁻a

If  ⁻b = ∧ ⁻a

then |⁻b| = |∧ ⁻a|

So one can say that  line ⁻b and ⁻a are  collinear.

2.  If ⁻a and ⁻b  are collinear

Assuming |b| length  is  'μ' times of |⁻a |

Then | 'μ' ⁻a| = | 'μ' ⁻a|

So  ⁻b = 'μ' ⁻a

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