In general, how would you sketch a vector that was n times a given vector? How would the lengths and headings?

Question

In general, how would you sketch a vector that was n times a given vector? How are the lengths and headings of these two vectors related?

Answer 1

The lengths would be n times as long as the original and the heading would be exactly the same.

Answer 2

if n is a scalar and not a vector then the length of the vector changes by a factor of n (new length = old length * n) and the direction remains constant.

If n is another vector with magnitude n and a direction then the vectors are multiplied using vector multiplication rules and the resultant will have a different magnitude and direction.

Answer 3

A scalar multiple of a vector is the same direction and 'scaled' in magnitude by the value.

That is, their 'headings' are the same, but their lengths are relative to the scalar by which they were multiplied.

Doug