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

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To calculate the norm of the vector

use the following formula:

where

is the dot product of the given vector with itself

Remember the dot product of the vector

with itself is:

Calculate the dot product of the radicand

Multiply

Add

Simplify if possible

So

Check:
Lets use Pythagorean's Theorem to check our work

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(0,0,4,0)),<BR>
green(line(4,0,4,-2)),<BR>
arrow(0,0,4,-2)<BR>
)

Plot of the vector (black line) with the vector components (green)
We can see that the vector has x and y components, which form the legs of the triangle. We can also see that the legs are 4 units and 2 units

Since we have a triangle with legs of 4 , 2 and a hypotenuse of x(our unknown side), we can use Pythagoreans theorem to find the unknown side.
Pythagoreans theorem
a^2+b^2=c^2

Plug in a=4 and b=2 and lets solve for c
1 6 + 4 = c ^ 2

Square each individual term

2 0 = c ^ 2

Combine like terms

s q r t ( 2 0 ) = s q r t ( c ^ 2 )

Take the square root of both sides

2*sqrt(5)=c

simplify

So the length of the hypotenuse is 2*sqrt(5)

. This verifies our answer