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Pada segitiga ABC, dengan titik P terletak di tengah antara titik B dan C, dan Q adalah titik berat segitiga tersebut. Jika u = A B dan v = A C , vektor QP ​ dinyatakan dalam u dan v adalah ....

Pada segitiga ABC, dengan titik P terletak di tengah antara titik B dan C, dan Q adalah titik berat segitiga tersebut. Jika  dan , vektor  dinyatakan dalam  dan   adalah ....

  1. 1 half left parenthesis u with rightwards arrow on top plus v with rightwards arrow on top right parenthesis

  2. 1 third left parenthesis u with rightwards arrow on top plus v with rightwards arrow on top right parenthesis

  3. 1 fourth left parenthesis u with rightwards arrow on top plus v with rightwards arrow on top right parenthesis

  4. 1 fifth left parenthesis u with rightwards arrow on top plus v with rightwards arrow on top right parenthesis

  5. 1 over 6 left parenthesis u with rightwards arrow on top plus v with rightwards arrow on top right parenthesis

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Pembahasan

Perhatikan gambar di bawah. Diketahui : dan . Karena Q adalah titik berat segitiga maka,

Perhatikan gambar di bawah.

Diketahui : begin mathsize 14px style u with rightwards arrow on top equals stack A B with rightwards arrow on top end style dan begin mathsize 14px style v with rightwards arrow on top equals stack A C with rightwards arrow on top end style. Karena Q adalah titik berat segitiga maka,

begin mathsize 14px style stack Q P with rightwards arrow on top equals 1 third stack A P with rightwards arrow on top end style

      begin mathsize 14px style equals 1 third space left parenthesis stack A C with rightwards arrow on top plus stack C P with rightwards arrow on top right parenthesis end style

      begin mathsize 14px style equals 1 third space open parentheses stack A C with rightwards arrow on top plus 1 half stack C B with rightwards arrow on top close parentheses end style

      begin mathsize 14px style equals 1 third space open parentheses stack A C with rightwards arrow on top plus 1 half left parenthesis stack C A with rightwards arrow on top plus stack A B right parenthesis with rightwards arrow on top close parentheses end style

      begin mathsize 14px style equals 1 third space open parentheses v with rightwards arrow on top plus 1 half left parenthesis negative v with rightwards arrow on top plus u with rightwards arrow on top right parenthesis close parentheses end style

      begin mathsize 14px style equals 1 third space v with rightwards arrow on top minus 1 over 6 v with rightwards arrow on top plus 1 over 6 u with rightwards arrow on top end style

      begin mathsize 14px style equals 1 over 6 v with rightwards arrow on top plus 1 over 6 u with rightwards arrow on top end style

      begin mathsize 14px style equals 1 over 6 left parenthesis v with rightwards arrow on top plus u with rightwards arrow on top right parenthesis end style

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Diketahui titik A(2,7,8) dan B(–1,1,–1). Jika Pmembagi ruas garis ABdengan perbandingan 2:1, maka vektor posisi p ​ adalah ....

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