How do you find the component form and magnitude of the vector v given initial point (-1,5) and terminal point (15, 12)?

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Answer 1 · 2017-03-24T23:00:02

Component form is v #= <16, 7>#
Magnitude is ||v|| = #sqrt305~~ 17.46#

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 = 5#

If terminal side is #(x_2, y_2)#

Then #x_2 = 15# and #y_2 = 12#

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

In this case, v #= < [15 - (-1)], (12 - 5)#

Which gives us v #= <16, 7>#

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(16^2+7^2#

||v|| = #sqrt(256+49)#

||v|| = #sqrt305#

||v||#~~ 17.46#