Question

Let u = <-4, 3>. Find the unit vector in the direction of u, and write your answer in component form. (2 points)

Answer 1

Answer:  < -4/5,  3/5>

This is equivalent to writing < -0.8, 0.6 >

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Explanation:

Draw an xy grid and plot the point (-4,3) on it. Draw a segment from the origin to this point. Then draw a vertical line until reaching the x axis. See the diagram below.

We have a right triangle with legs of 4 and 3. The hypotenuse is $\sqrt{4^2+3^2} = \sqrt{16+9} = \sqrt{25} = 5$ through use of the pythagorean theorem.

We have a 3-4-5 right triangle.

Therefore, the vector is 5 units long. This is the magnitude of the vector.

Divide each component by the magnitude so that the resulting vector is a unit vector pointing in this same direction.

Therefore, we go from < -4, 3 > to < -4/5,  3/5 >

This is equivalent to < -0.8, 0.6 > since -4/5 = -0.8 and 3/5 = 0.6

Side note: Unit vectors are useful in computer graphics.