Jika vektor a=([1],[2],[3]), b=([5],[4],[-1]), dan c=([4],[-1],[1]), maka vektor a+2b-3c=.... A. 6i+11j-8k B. 7i+13j-8k C. -i+12j-2k D. -i+13j-2k E. -6i-12j+8k

<p>Jawaban :<strong> D. −i + 13j – 2k</strong></p><p><strong>&nbsp;</strong></p><p>Diketahui :</p><p>a = (1, 2, 3)</p><p>b = (5, 4, −1)</p><p>c = (4, −1, 1)</p><p>&nbsp;</p><p>Ditanya : vektor a + 2b – 3c</p><p>&nbsp;</p><p>Ingat !</p><p>·&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Penjumlahan &amp; Pengurangan vektor</p><p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;a ± b = (a_{1 ,} a_2,a₃) ± (b_{1 ,} b_2,b₃) = (a₁± b_1, a₂± b_2,a₃± b₃)</p><p>·&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Perkalian vektor dengan skalar</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp;Jika a = (a_{1 ,} a_2,a₃) dan k adalah skalar , maka ka = (ka_{1 ,} ka_2,ka₃)</p><p>&nbsp;</p><p>Jawab :</p><p>a = (1, 2, 3)</p><p>&nbsp;</p><p>b = (5, 4, −1), maka 2b = (2×5, 2×4, 2×(−1))</p><p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp;&nbsp; &nbsp; &nbsp; 2b = (10, 8, −2)</p><p>&nbsp;</p><p>c = (4, −1, 1), maka 3c = (3×4, 3×(−1), 3×1)</p><p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp;&nbsp; &nbsp; &nbsp; 3c = (12, −3, 3)</p><p>&nbsp;</p><p>Sehingga :</p><p>a + 2b – 3c = (1, 2, 3) + (10, 8, −2) − (12, −3, 3)</p><p>a + 2b – 3c = (1+10−12, 2+8−(−3), 3+(−2) −3)</p><p>a + 2b – 3c = (−1, 13, −2)</p><p>maka jika diubah ke bentuk vektor basis i, j, k &nbsp;:</p><p>a + 2b – 3c = −i + 13j – 2k</p><p>&nbsp;</p><p>Jadi, vektor a + 2b – 3c adalah <strong>−i + 13j – 2k</strong></p>