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adalah jajargenjang dengan , titik  dan  masing-ma...

begin mathsize 14px style A B C D end style adalah jajargenjang dengan begin mathsize 14px style stack A B with rightwards arrow on top equals u with rightwards arrow on top comma space stack A D with rightwards arrow on top equals v with rightwards arrow on top end style, titik begin mathsize 14px style E end style dan begin mathsize 14px style F end style masing-masing titik tengah begin mathsize 14px style stack D C with rightwards arrow on top end style dan begin mathsize 14px style stack B C with rightwards arrow on top end style. Nyatakan vektor-vektor berikut dalam begin mathsize 14px style u with rightwards arrow on top end style dan begin mathsize 14px style v with rightwards arrow on top end style.

b.  begin mathsize 14px style stack E F with rightwards arrow on top end style 

Jawaban:

Ilustrasi untuk soal di atas adalah sebagai berikut:



Untuk vektor begin mathsize 14px style stack E C with rightwards arrow on top end style didapatkan:

begin mathsize 14px style stack E C with rightwards arrow on top equals 1 half stack D C with rightwards arrow on top stack E C with rightwards arrow on top equals 1 half u with rightwards arrow on top end style 

Untuk vektor begin mathsize 14px style stack C F with rightwards arrow on top end style didapatkan:

begin mathsize 14px style stack C F with rightwards arrow on top equals 1 half stack C B with rightwards arrow on top stack C F with rightwards arrow on top equals 1 half left parenthesis negative v with rightwards arrow on top right parenthesis stack C F with rightwards arrow on top equals negative 1 half v with rightwards arrow on top end style  

Sehingga, vektor begin mathsize 14px style stack E F with rightwards arrow on top end style didapatkan:

begin mathsize 14px style stack E F with rightwards arrow on top equals stack E C with rightwards arrow on top plus stack C F with rightwards arrow on top stack E F with rightwards arrow on top equals 1 half u with rightwards arrow on top minus 1 half v with rightwards arrow on top stack E F with rightwards arrow on top equals 1 half open parentheses u with rightwards arrow on top minus v with rightwards arrow on top close parentheses end style 

Dengan demikian, vektor begin mathsize 14px style stack E F with rightwards arrow on top end style dalam begin mathsize 14px style u with rightwards arrow on top end style dan begin mathsize 14px style v with rightwards arrow on top end style adalah begin mathsize 14px style 1 half open parentheses u with rightwards arrow on top minus v with rightwards arrow on top close parentheses end style.

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