A vector starts at (9, 9) and terminates at (0, -4). A second vector starts at the origin and terminates at (-1, 6).

Question

A vector starts at (9, 9) and terminates at (0, -4). A second vector starts at the origin and terminates at (-1, 6). What is the absolute difference in their magnitudes?

Answer 1

The "magnitude" of a vector is basically the length of that vector. The length of the vector can be found using the nifty Pythagorean theorem. Let's call the first vector, vector A. Use this formula to find the magnitude.

 

|A| = √[(x₂ - x₁)² + (y₂ - y₁)²]

|A| = √[(0 - 9)² + (-4 - 9)²]

|A| = √[(-9)² + (-13)²]

|A| = √(81 + 169)

|A| = √250

|A| = 5√10

 

Now do the same stuff with the Pythagorean theorem for the second vector, which we'll call vector B. This one goes from (0, 0) to (-1, 6).

 

|B| = √[(x₂ - x₁)² + (y₂ - y₁)²]

|B| = √[(-1 - 0)² + (6 - 0)²]

|B| = √[(-1)² + (6)²]

|B| = √(1 + 36)

|B| = √37

 

The absolute difference can be found by subtracting the two magnitudes.

 

5√10 - √37 ≈ 9.7

 

I hope this helps, and good luck with your math class!