To add or subtract 2 vectors, include or subtract the corresponding components.

permit u → = 〈 u 1 , u 2 〉 and v → = 〈 v 1 , v 2 〉 be 2 vectors.

Then, the amount of u → and also v → is the vector

u → + v → = 〈 u 1 + v 1 , u 2 + v 2 〉

The difference of u → and v → is

u → − v → = u → + ( − v → )                       = 〈 u 1 − v 1 , u 2 − v 2 〉

The sum of two or more vectors is referred to as the resultant. The resultant of 2 vectors have the right to be discovered using one of two people the parallelogram technique or the triangle technique .

parallelogram Method:

draw the vectors so that their initial points coincide. Then attract lines to form a complete parallelogram. The diagonal from the initial point to the opposite vertex of the parallel is the resultant.

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Vector Addition:

ar both vectors u → and v → at the very same initial point. complete the parallelogram. The resultant vector u → + v → is the diagonal of the parallelogram.

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Vector Subtraction:

complete the parallelogram. attract the diagonals of the parallel from the early point.

Triangle Method:

attract the vectors one ~ another, placing the initial point of each succeeding vector at the terminal suggest of the previous vector. Then attract the resultant from the initial point of the an initial vector to the terminal point of the critical vector. This method is likewise called the head-to-tail technique .

Vector Addition:

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Vector Subtraction:

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Example:

find (a) u → + v → and (b) u → − v → if u → = 〈 3 , 4 〉 and also v → = 〈 5 , − 1 〉 .

substitute the provided values that u 1 , u 2 , v 1 and v 2 into the definition of vector addition.

u → + v → = 〈 u 1 + v 1 , u 2 + v 2 〉                       = 〈 3 + 5 , 4 + ( − 1 ) 〉                       = 〈 8 , 3 〉

Rewrite the distinction u → − v → together a amount u → + ( − v → ) . Us will require to identify the materials of − v → .

Recall that − v → is a scalar many of − 1 times v .

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Indigenous the an interpretation of scalar multiplication, us have:

− v → = − 1 〈 v 1 , v 2 〉               = − 1 〈 5 , − 1 〉               = 〈 − 5 , 1 〉

Now add the components of u → and also − v → .

u → + ( − v → ) = 〈 3 + ( − 5 ) , 4 + 1 〉                                     = 〈 − 2 , 5 〉