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

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Answer 1 · 2017-03-28T20:14:33

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

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#