How do you find the component form and magnitude of the vector v given initial point (1,3) and terminal point (-8,-9)?

1 Answer
Mar 28, 2017

Component form is v = <-9, -12>
Magnitude is ||v|| = 15

Explanation:

To find the component form, you only need to know how to substitute figures for letters. What do I mean by this?

If initial side is (x_1, y_1)

Then x_1 =1 and y_1 = 3

If terminal side is (x_2, y_2)

Then x_2 = -8 and y_2 = -9

Thus, component form of v is < (x_2 - x_1), (y_2 - y_1) >...simply <x, y>

In this case, v = < [(-8) -1], [(-9) - 3]

Which gives us v = <-9, -12>

To find the magnitude of a vector, the concept of pythagorean theorem needs to be understood.

Why?

If v= <x, y>, using pythagorean theorem, ||v||= sqrt(x^2+ y^2)

We already know the values for v, so;

||v|| = sqrt((-9)^2+(-12)^2)

||v|| = sqrt(81+144)

||v|| = sqrt225

||v||= 15