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What is meant by subtraction of vectors? |
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Answer» SOLUTION :For two non-zero vectors consider `vec(A) and vec(B)`that are inclined to each other at an ANGLE `theta` , the difference `vec(A) - vec(B)`is obtained as follows . first obtain ` - vec(B)`as in figure (SUBTRACTION of vectors) . The angle between `vec(A) and - vec(B)`is`180 - theta` . The difference `vec(A) - vec(B)`is the same as the resultant of `vec(A) and - vec(B)` We can write `vec(A) - vec(B) = vec(A) + (-vec(B)) `and using the equation , we get `|vec(A)- vec(B)| = sqrt(A^(2) +B^(2)+2A B cos (180 - theta))` Since , cos `(180 - theta) = - cos theta `, we get `|vec(A) - vec(B)| = sqrt(A^(2) +B^(2) - 2 ABcos theta)` Again from the figure, and the equation similar to the equation `tan alpha_(2) = (B sin ( 180^(@) - theta))/(A + B cos (180^(@)- theta))` But , sin `(180^(@) - theta) = sin theta`HENCE we get `:. tan alpha_(2) = (B sin theta)/(A - B cos theta)` 
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