diketahui a = 2i + 3j + k dan b = -i + 2j + pk. agar (a+b) tegak lurus 6(a-b) maka nilai p adalah

Agar tegak lurus, (a+b).(6(a-b)) = 0

[tex]\left[\begin{array}{ccc}2+(-1)\\3+2\\1+p\end{array}\right] . 6\left[\begin{array}{ccc}2-(-1)\\3-2\\1-p\end{array}\right] = 0 \\ \\ \\ \left[\begin{array}{ccc}1\\5\\1+p\end{array}\right] . \left[\begin{array}{ccc}18\\6\\6-6p\end{array}\right] = 0[/tex]

1.18 + 5.6 + (1+p)(6-6p) = 0
18 + 30 + (-6p²+6) = 0
48 + (-6p²+6) = 0
-6p² = - 54
p² = 9
p = ±3