Pertanyaan

Diketahui titik A(1, 0, –2), B(2, 1, –1), C(2, 0, –3). Sudut antara vektor AB dengan AC adalah ….

Diketahui titik A(1, 0, –2), B(2, 1, –1), C(2, 0, –3). Sudut antara vektor $AB$ dengan $AC$ adalah ….

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Pembahasan

Diketahui titik A(1, 0, –2), B(2, 1, –1), C(2, 0, –3), maka: Misal sudut antara vektor dengan adalah maka:

Diketahui titik A(1, 0, –2), B(2, 1, –1), C(2, 0, –3), maka:

Misal sudut antara vektor begin mathsize 14px style AB with rightwards arrow on top end style dengan begin mathsize 14px style AC with rightwards arrow on top end style adalah begin mathsize 14px style straight alpha end style maka:

$begin mathsize 14px style cos space straight alpha equals fraction numerator AB with rightwards arrow on top space. space AC with rightwards arrow on top over denominator open vertical bar AB with rightwards arrow on top close vertical bar space stack open vertical bar AC close vertical bar with rightwards arrow on top end fraction equals fraction numerator open parentheses table row 1 row 1 row 1 end table close parentheses space. space open parentheses table row 1 row 0 row cell negative 1 end cell end table close parentheses over denominator open parentheses square root of 1 squared plus 1 squared plus 1 squared end root close parentheses space open parentheses square root of 1 squared plus 0 squared plus 1 squared end root close parentheses end fraction equals fraction numerator 1 plus 0 minus 1 over denominator square root of 3. space square root of 2 end fraction equals 0 cos space straight alpha equals 0 rightwards arrow straight alpha equals 90 degree end style$