Question

prove that following points (2,-1,-3),(5,1,-1)and(-1,-3,-5)​

Answer 1

Answer:

step by step explanation

Let points (−2,3,5),(1,2,3) and (7,0,−1) be denoted by P,Q and R respectively.

Points P,Q and R are collinear if they lie on a line.

PQ=

(1+2)

2

+(2−3)

2

+(3−5)

2

=

(3)

2

+(−1)

2

+(−2)

2

=

9+1+4

=

14

QR=

(7−1)

2

+(0−2)

2

+(−1−3)

2

=

(6)

2

+(−2)

2

+(−4)

2

=

36+4+16

=

56

=2

14

PR=

(7+2)

2

+(0−3)

2

+(−1−5)

2

=

(9)

2

+(−3)

2

+(−6)

2

=

81+9+36

=

126

=3

14

Here PQ+QR=

14

+2

14

=3

14

=PR

⇒PQ+QR=PR

Hence points P(−2,3,5),Q(1,2,3) and R(7,0,−1) are collinear