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Question

The points (2,3,5),(1,2,3) and (7,0,1) form

A
a straight line.
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B
an isosceles triangle
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C
a right angled triangle
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D
an equilateral triangle
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Solution

The correct option is A a straight line.
Given: Points (2,3,5),(1,2,3) and (7,0,1)
Let the points be P,Q and R respectively.
Applying Distance formula
=(x2x1)2+(y2y1)2+(z2z1)2
PQ=(1+2)2+(23)2+(35)2=14
QR=36+4+16=56=214
PR=(7+2)2+(03)2+36=126=314
For triangle to form sum of any two sides > third side But,
Clearly, PQ+QR=PR
Hence P,Q,R are collinear points.

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