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Diketahui titik  dan titik . Perhatikan pernyataan...

Diketahui titik A open parentheses 1 comma 6 close parentheses dan titik straight B open parentheses 7 comma 8 close parentheses. Perhatikan pernyataan-pernyataan berikut!

(i). Vektor stack A B with rightwards arrow on top adalah 6 i with hat on top plus 2 j with hat on top

(ii). Vektor stack B A with rightwards arrow on top adalah open parentheses 5 comma space 2 close parentheses

(iii). Modulus vektor stack A B with rightwards arrow on top  adalah 2 square root of 10 

(iv). Panjang vektor stack B A with rightwards arrow on top adalah square root of 29 

Pernyataan yang benar ditunjukkan oleh ...

  1. (i) dan (ii)

  2. (i) dan (iii)

  3. (ii) dan (iii)

  4. (ii) dan (iv)

  5. (iii) dan (iv)

Jawaban:

Diketahui titik A open parentheses 1 comma 6 close parentheses dan titik straight B open parentheses 7 comma 8 close parentheses. Maka:

table attributes columnalign right center left columnspacing 0px end attributes row cell stack A B with rightwards arrow on top end cell equals cell B minus A end cell row blank equals cell left parenthesis 7 comma space 8 right parenthesis minus left parenthesis 1 comma space 6 right parenthesis end cell row blank equals cell left parenthesis 7 minus 1 comma space 8 minus 6 right parenthesis end cell row blank equals cell left parenthesis 6 comma space 2 right parenthesis end cell row blank equals cell 6 i with hat on top plus 2 j with hat on top end cell row blank blank blank row cell open vertical bar stack A B with rightwards arrow on top close vertical bar end cell equals cell square root of 6 squared plus 2 squared end root end cell row blank equals cell square root of 36 plus 4 end root end cell row blank equals cell square root of 40 end cell row blank equals cell 2 square root of 10 end cell row blank blank blank row cell stack B A with rightwards arrow on top end cell equals cell A minus B end cell row blank equals cell left parenthesis 1 comma space 6 right parenthesis minus left parenthesis 7 comma space 8 right parenthesis end cell row blank equals cell left parenthesis 1 minus 7 comma space 6 minus 8 right parenthesis end cell row blank equals cell left parenthesis negative 6 comma space minus 2 right parenthesis end cell row blank equals cell negative 6 i with hat on top minus 2 j with hat on top end cell row blank blank blank row cell open vertical bar stack B A with rightwards arrow on top close vertical bar end cell equals cell square root of left parenthesis negative 6 right parenthesis squared plus left parenthesis negative 2 right parenthesis squared end root end cell row blank equals cell square root of 36 plus 4 end root end cell row blank equals cell square root of 40 end cell row blank equals cell 2 square root of 10 end cell row blank blank blank end table 

Sehingga:

(i). Vektor stack A B with rightwards arrow on top adalah 6 i with hat on top plus 2 j with hat on top (benar)

(ii). Vektor stack B A with rightwards arrow on top adalah open parentheses 5 comma space 2 close parentheses (salah)

(iii). Modulus vektor stack A B with rightwards arrow on top  adalah 2 square root of 10 (benar)

(iv). Panjang vektor stack B A with rightwards arrow on top adalah square root of 29 (salah)

Maka, pernyataan yang benar ditunjukkan oleh (i) dan (iii).

Jadi, jawaban yang tepat adalah B

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