To add or subtract two vectors, add or subtract the corresponding components.

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

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

u → + v → = 〈 u 1 + v 1 , u 2 + v 2 〉

The difference of u → and also v → is

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

The amount of two or much more vectors is called the resultant. The result of two vectors have the right to be found using one of two people the parallelogram method or the triangle an approach .

parallelogram Method:

draw the vectors so that their initial clues coincide. Then attract lines to type a finish parallelogram. The diagonal line from the initial suggest to the opposite vertex of the parallelogram is the resultant.

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Vector Addition:

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

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Vector Subtraction:

finish the parallelogram. draw the diagonals of the parallel from the initial point.

Triangle Method:

attract the vectors one after another, put the initial allude of each succeeding vector in ~ the terminal point of the vault vector. Then draw the result from the initial suggest of the very first vector to the terminal allude of the last vector. This technique is also 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 〉 .

instead of the offered values of u 1 , u 2 , v 1 and v 2 into the an interpretation of vector addition.

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

Rewrite the difference u → − v → as a amount u → + ( − v → ) . Us will need to recognize the contents of − v → .

Recall the − v → is a scalar multiple of − 1 times v .

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Native the meaning of scalar multiplication, us have:

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

Now include the materials of u → and − v → .

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