Question

The tail of a vector is at (2, 4). The head of the same vector is at (5, 2). What is the algebraic description of this vector? [Sketch the problem if you need help visualizing it.]

Answer 1

Explanation:

Given that:

• Tail: (2, 4)

• Head: (5, 2)

The vector is the straight line, so to form the algebraic description of this vector we need to find out the slope of it:

Slope:
`(y2-y1)/(x2-x1)` =
`(2-4)/(5-2)` =
`(-2)/(3)`

We have the standard form of the linear is:

y = mx +b

In this situation, y =
`(-2)/(3)`x + b (1)

Because the line go through the point: (2, 4) so we substitute them into the equation (1): 4 =
`(-2)/(3)` (2) + b <=> b =
`(16)/(3)`

So the algebraic description of this vector is: y =
`(-2)/(3)`x +
`(16)/(3)`