InterviewSolution
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InterviewSolution
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`A B C D`is parallelogram and `P`is the point of intersection of its diagonals. If `O`is the origin of reference, show that ` vec O A+ vec O B+ vec O C+ vec O D=4 vec O Pdot` |
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Answer» Please refer to video to see the vector diagram for the given details. From the diagram,`vec(OD) + vec(DP) = vec(OP)` `vec(OA) + vec(AP) = vec(OP)` `vec(OB) + vec(BP) = vec(OP)` `vec(OC) + vec(CP) = vec(OP)` `:. vec(OD) + vec(DP)+vec(OA) + vec(AP)+vec(OB) + vec(BP)+vec(OC) + vec(CP) = 4vec(OP)` `=>vec(OA)+vec(OB)+vec(OC)+vec(OD)+vec(AP)+vec(CP)+vec(BP)+vec(DP) = 4vec(OP)->(1)` Also, from the diagram, we can see that, `vec(PA)+vec(PC) = 0` `vec(PD)+vec(PB) = 0` So, equation (1) becomes, `=>vec(OA)+vec(OB)+vec(OC)+vec(OD) + 0 + 0 = 4vec(OP)` `=>vec(OA)+vec(OB)+vec(OC)+vec(OD) = 4vec(OP)` |
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