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Question

Find the sum of the vectors $$\vec {a} = \hat {i} - 2\hat {j} +\hat {k} = -2\hat {i} + 4\hat {j} + 5\hat {k}$$ and $$\vec {c} = \hat {i} - 6\hat {j} - 7\hat {k}.$$


Solution

Add the vectors $$\vec { a } =\hat { i } -2\hat { j } +\hat { k } \\$$, $$\vec { b } =-2\hat { i } +4\hat { j } +5\hat { k } \\$$ and $$\vec { c } =\hat { i } -6\hat { j } -7\hat { k }$$  by writing them in the component form that is

$$\vec { a } =\left< 1,-2,1 \right> \\$$, $$\vec { b } =\left< -2,4,5 \right> \\$$ and $$\vec { c } =\left< 1,-6,-7 \right>$$ 

Then the sum of the vectors can be computed as follows:

$$\vec { a } +\vec { b } +\vec { c } =\left< 1-2+1,-2+4-6,1+5-7 \right> \\$$ 

                 $$=\left< 0,-4,-1 \right>$$ 

Hence the sum of the vectors is $$\left< 0,-4,-1 \right> =-4\hat { j } -\hat { k }. \\.$$

Mathematics

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