Question

consider u = (5, -2) and v = (10, -4). what is the relationship between u and v? the vectors point in the same direction. the vectors form an acute angle. the vectors form an obtuse angle. the vectors point in opposite directions.

Explanation:

Step1: Check if vectors are scalar multiples

If \(v = k\times u\), where \(k\) is a scalar.
Given \(u=\langle5,-2
angle\) and \(v = \langle10,-4
angle\). Let's find \(k\) for the \(x -\) component: \(10=k\times5\), so \(k = 2\).
For the \(y -\) component: \(-4=k\times(-2)\), substituting \(k = 2\) gives \(-4=2\times(-2)\) which is true.

Step2: Analyze direction

Since \(k=2>0\), when \(v=k\times u\) and \(k>0\), the vectors \(u\) and \(v\) have the same direction.

Answer:

The vectors point in the same direction.