Questions on Algebra: Introduction to vectors, addition and scaling answered by real tutors!

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Question 88102: find the magnitude of the following vector:
v=3i-2j: find the magnitude of the following vector:
v=3i-2j
Answer by jim_thompson5910(9162) About Me  (Show Source):
You can put this solution on YOUR website!
To calculate the norm of the vector use the following formula:

where is the dot product of the given vector with itself


Calculate the dot product of the radicand

Multiply

Add


So

Notice if we draw the vector we get
drawing(500, 500, -5+2, 5+2, -5+2, 5+2,<BR> graph(500, 500, -5+2, 5+2, -5+2, 5+2, 0),<BR> green(line(0,0,3,0)),<BR> green(line(3,0,3,-2)),<BR> arrow(0,0,3,-2)) <BR> <BR> ) Plot of the vector (black line) with the vector components (green)
and if we used Pythagorean's Theorem, we would find that the magnitude is