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Diketahui titik A(5,-3), B(-2,-7), dan C(-6,1). Tentukan !

Pertanyaan

Diketahui titik A(5,-3), B(-2,-7), dan C(-6,1). Tentukan begin mathsize 14px style open parentheses AB with rightwards arrow on top plus BC with rightwards arrow on top close parentheses plus stack A C with rightwards arrow on top end style!

Pembahasan Soal:

vektor posisi dari titik A, B, dan C masing-masing sebagai berikut.

stack size 14px O size 14px A with size 14px rightwards arrow on top size 14px equals size 14px a with size 14px rightwards arrow on top size 14px equals begin mathsize 14px style left parenthesis 5 comma negative 3 right parenthesis end style stack size 14px O size 14px B with size 14px rightwards arrow on top size 14px equals size 14px b with size 14px rightwards arrow on top size 14px equals begin mathsize 14px style left parenthesis negative 2 comma negative 7 right parenthesis end style size 14px space stack size 14px O size 14px C with size 14px rightwards arrow on top size 14px equals size 14px c with size 14px rightwards arrow on top size 14px equals begin mathsize 14px style left parenthesis negative 6 comma 1 right parenthesis end style 

maka  begin mathsize 14px style AB with rightwards arrow on top comma space BC with rightwards arrow on top comma space end style dan begin mathsize 14px style AC with rightwards arrow on top end style

begin mathsize 14px style AB with rightwards arrow on top equals b with rightwards arrow on top minus a with rightwards arrow on top space space space space space space equals left parenthesis negative 2 comma negative 7 right parenthesis minus left parenthesis 5 comma negative 3 right parenthesis space space space space space space equals left parenthesis negative 2 minus 5 comma negative 7 plus 3 right parenthesis space space space space space space equals left parenthesis negative 7 comma negative 4 right parenthesis BC with rightwards arrow on top equals c with rightwards arrow on top minus b with rightwards arrow on top space space space space space space equals left parenthesis negative 6 comma 1 right parenthesis minus left parenthesis negative 2 comma negative 7 right parenthesis space space space space space space equals left parenthesis negative 6 plus 2 comma 1 plus 7 right parenthesis space space space space space space equals left parenthesis negative 4 comma 8 right parenthesis stack A C with rightwards arrow on top equals c with rightwards arrow on top minus a with rightwards arrow on top space space space space space equals open parentheses negative 6 comma 1 close parentheses minus open parentheses 5 comma negative 3 close parentheses space space space space space equals open parentheses negative 6 minus 5 comma 1 plus 3 close parentheses space space space space space equals open parentheses negative 11 comma 4 close parentheses end style  

Selanjutnya akan ditentukan  begin mathsize 14px style open parentheses AB with rightwards arrow on top plus BC with rightwards arrow on top close parentheses plus stack A C with rightwards arrow on top end style

begin mathsize 14px style stack A B with rightwards arrow on top plus stack B C with rightwards arrow on top equals left parenthesis negative 7 comma negative 4 right parenthesis plus left parenthesis negative 4 comma 8 right parenthesis space space space space space space space space space space space space space space equals left parenthesis negative 7 minus 4 comma negative 4 plus 8 right parenthesis space space space space space space space space space space space space space space equals left parenthesis negative 11 comma 4 right parenthesis open parentheses stack A B with rightwards arrow on top plus stack B C with rightwards arrow on top close parentheses plus stack A C with rightwards arrow on top equals left parenthesis negative 11 comma 4 right parenthesis plus open parentheses negative 11 comma 4 close parentheses space space space space space space space space space space space space space space space space space space space space space space space space equals open parentheses negative 22 comma 8 close parentheses end style 

Jadi, begin mathsize 14px style open parentheses AB with rightwards arrow on top plus BC with rightwards arrow on top close parentheses plus stack A C with rightwards arrow on top end style = begin mathsize 14px style open parentheses negative 22 comma 8 close parentheses end style 

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 04 April 2021

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