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

Answer:

Step-by-step 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: $\frac{y2-y1}{x2-x1}$ = $\frac{2-4}{5-2}$ = $\frac{-2}{3}$

We have the standard form of the linear is:

y = mx +b

In this situation, y = $\frac{-2}{3}$x + b (1)

Because the line go through the point: (2, 4) so we substitute them into the equation (1):  4 = $\frac{-2}{3}$ (2) + b <=> b = $\frac{16}{3}$

So  the algebraic description of this vector is:  y = $\frac{-2}{3}$x + $\frac{16}{3}$