Given 2 vectors A = 4.00i + 3.00j and B =5.00i - 2.00 j how do you find the magnitude & direction of the vector difference A - B?

1 Answer
Gió
Jan 24, 2016

We can subtract directly the corresponding components and check using the parallelogram rule.

Explanation:

Have a look:
enter image source here
Where, graphically, I used the fact that:
vecA-vecB=vecA+(-vecB)

For the magnitude we use Pythagoras (with the components) to get:
|vecA-vecB|=sqrt((-1)^2+(5)^2)=sqrt(1+25)=sqrt(26)~~5.1

For the direction I can see that will be 90^@ from the x axis up to the y axis, plus the little bit passed the y axis given as:
theta=arctan(1/5)=11.3^@
giving in total: angle=90^@+11.3^@=101.3^@

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