Solution.
(4.1)A=(−1;0;1),B=(0;−2;3),C=(−4;4;1);
AB=(0+1)2+(−2−0)2+(3−1)2=3;
BC=(−4−0)2+(4+2)2+(1−3)2=56=214;
AC=(−4+1)2+(4−0)2+(1−1)2=5;
(4.2)P=(3;1;−1),Q=(2;0;3),R=(1;1;1)
PQ=(2−3)2+(0−1)2+(3+1)2=32;
QR=(1−2)2+(1−0)2+(1−3)2=6;
PR=(1−3)2+(1−1)2+(1+1)2=22;
PQ2=QR2+PR2;
18=6+8;18=14, therefore, the triangle is not right-angled.
Answer: (4.1)AB=3;BC=214;AC=5;
(4.2) A triangle is not right-angled because Pythagoras' theorem does not hold.
Comments