Answer:
a. FALSE
b.TRUE
C. FALSE
Explanation:
The formula fot the distance between two points is given as
[tex]d=\sqrt{(x_{2}-x_{1})^{2} +(y_{2}-y_{1})^{2} +(z_{2}-z_{1})^{2}}\\[/tex]
hence we determine the distances between all the points
a.P(3,2,-4), Q(1,0,-4), R(2,1,1)
[tex]PQ=\sqrt{(1-3)^{2} +(0-2)^{2} +(-4-(-4))^{2}}\\PQ=\sqrt{4+4+0}\\ PQ=\sqrt{8}[/tex]
For point PR
we have
[tex]PR=\sqrt{(2-3)^{2} +(1-2)^{2} +(1-(-4))^{2}}\\PR=\sqrt{1+1+9}\\ PR=\sqrt{11}\\[/tex]
[tex]|PQ|\neq |PR|[/tex]
B. For point RP
[tex]RP=\sqrt{(3-2)^{2} +(2-1)^{2} +(-4-1)^{2}}\\RP=\sqrt{1+1+25}\\ RP=\sqrt{27}[/tex]
for point RQ we have
[tex]RQ=\sqrt{(1-2)^{2} +(0-1)^{2} +(-4-1)^{2}}\\RQ=\sqrt{1+1+25}\\ RQ=\sqrt{27}[/tex]
|RP|=|R Q|
C.
[tex]QP=\sqrt{(3-1)^{2} +(2-0)^{2} +(-4+4)^{2}}\\QP=\sqrt{4+4+0}\\ QP=\sqrt{8}[/tex]
For point Q R
[tex]QR=\sqrt{(2-1)^{2} +(1-0)^{2} +(1-(-4))^{2}}\\QR=\sqrt{1+1+9}\\ QR=\sqrt{11}\\[/tex]
[tex]QP\neq QR[/tex]
