Question

URGENTE 

Dados os pontos A(-1,0,5), B(2,-1,4), C(1,1,1), determinar x tal q AC e BP seja ortogonais,sendo P(x,0,x-3)?

Answer 1

$A=(-1;0;5)\\\\B=(2;-1;4)\\\\C=(1;1;1)\\\\P=(X;0;X-3)$

AC = C -A 
$AC=(1;1;1)-(-1;0;5)\\\\AC=(1-(-1));(1-0);(1-5)\\\\AC=(2;1;-4)$

BP = P-B
$BP=(X;0;X-3)-(2;-1;4)\\\\BP=(X-2);(0-(-1));(X-3-4)\\\\BP=(X-2;1;X-7)$

ELE QUER QUE AC E BP SEJAM ORTOGONAIS
para isso acontecer o produto escalar entre eles tem que dar 0
então 
$AC*BP=0\\\\(2;1;-4)*(X-2;1;X-7)=0\\\\(2*(X-2))+(1*1)+(-4*(X-7))=0\\\\(2X-4)+(1)+(-4X+28)=0\\\\2X-4+1-4X+28=0\\\\(2X-4X)+(-4+1+28)=0\\\\-2X+25=0\\\\X= \frac{-25}{-2} \\\\\boxed{X= \frac{25}{2} }$