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Q.

Vector A extends from the origin to a point having position coordinates represented in different way like (7,70) and vector B extends from the origin to a point having position coordinates in different way like (4,100) and both are in XY plane. Find    area of triangle formed by A¯B¯ vectors as adjacent sides. (given angle in the co ordinates it is with positive x – axis)

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answer is 7.

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Detailed Solution

We can use 12(A×B). We have the magnitudes of the two vectors (namely A=7 and B= 4) and the angle ϕ between the two is ϕ=10070=30.  
Then we get: 12(A×B)=12ABsinϕ=(7)(4)=12sin30142=7 

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