If P(2,3,4), Q(-1,-2,1) and R(5,8,7) are three points, then - Vidyadip

MCQ

If $P(2,3,4), Q(-1,-2,1)$ and $R(5,8,7)$ are three points, then

A
direction ratios of $P Q$ and $Q R$ are not in proportion
B
$P, Q, R$ lie on the same line
C
$P, Q, R$ do not lie on the same line
D
None of these

✓

Answer

(b) : Given points are $P(2,3,4), Q(-1,-2,1)$ and $R(5,8,7)$.
Direction ratios of $P Q$ are $(-1-2,-2-3,1-4)$, i.e., ( -3 , $-5,-3$)
Direction ratios of $Q R$ are $(5+1,8+2,7-1)$, i.e., (6, 10,6 )
As $\frac{-3}{6}=\frac{-5}{10}=\frac{-3}{6}$, therefore the direction ratios of $P Q$ and $Q R$ are proportional.
Hence, $P Q$ and $Q R$ are parallel but they have a point $Q$ in common. Therefore $P Q$ and $Q R$ are along the same line i.e., $P, Q$ and $R$ are collinear.

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