which of the following pairs of points have a distance  $\sqrt{43}$ ?

detailed solution

Correct option is A

(a) Let the given points are A(2,3,5) and B(4,3,1).      ∴    x1=2,y1=3,z1=5 and     x2=4,y2=3,z2=1      Required distance      AB=x2−x12+y2−y12+z2−z12⇒  AB=(4−2)2+(3−3)2+(1−5)2=4+0+16=20=25(b) Let the given points are A(- 3,7,2) and B(2,4, -1).        Here,      x1=−3,y1=7,z1=2x2=2,y2=4,z2=−1         Required distance         AB=x2−x12+y2−y12+z2−z12=[2−(−3)]2+(4−7)2+(−1−2)2=(2+3)2+(4−7)2+(−1−2)2=25+9+9=43(c)  Let the given ,points  (-1, 3, -4) and (1, -3, 4)       x1=−1,y1=3,z1=−4x2=1,y2=−3,z2=4       Required distance,       AB=(1+1)2+(−3−3)2+(4+4)2=4+36+64=104=226(d) Let the given points are A(2, -1,3) and B(-2,1,3).       x1=2,y1=−1,z1=3x2=−2,y2=1,z2=3         Required distance,        AB=(−2−2)2+(1+1)2+(3−3)2=42+22+0=16+4=20=25