diketahui vektor a=i+2j-xk vektor b=3i-2j+k dan c=2i+j+2k. jika a tegak lurus c maka (a+b).(a-c) hasilnya adalah

diketahui vektor a=i+2j-xk vektor b=3i-2j+k dan c=2i+j+2k. jika a tegak lurus c maka (a+b).(a-c) hasilnya adalah

Jawaban Terkonfirmasi

Kode : 12.2.4 [Kelas 12 Matematika BAB 4 – Vektor]

Diketahui
$a= left[begin{array}{ccc}1\2\-xend{array}right] \b= left[begin{array}{ccc}3\-2\1end{array}right] \c = left[begin{array}{ccc}2\1\2end{array}right]$

Karena saling tegak lurus, $a.c=0$
Sehingga
$left[begin{array}{ccc}1\2\-xend{array}right] . left[begin{array}{ccc}2\1\2end{array}right]=0$
(1)(2) + (2)(1) + (-x)(2) = 0
4 = 2x
x = 2
Jadi vektor $a= left[begin{array}{ccc}1\2\-2end{array}right]$

Siapkan a + b
$a+b= left[begin{array}{ccc}1\2\-2end{array}right]+ left[begin{array}{ccc}3\-2\1end{array}right] = left[begin{array}{ccc}4\0\-1end{array}right]$
Siapkan a – c
$a-c= left[begin{array}{ccc}1\2\-2end{array}right]- left[begin{array}{ccc}2\1\2end{array}right] = left[begin{array}{ccc}-1\1\-4end{array}right]$

(a + b).(a – c) = ?

$left[begin{array}{ccc}4\0\-1end{array}right] . left[begin{array}{ccc}-1\1\-4end{array}right] =(4)(-1)+(0)(1)+(-1)(-4)$

Jadi (a + b).(a – c) = 0.