Question

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

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

Answer 1

The correct option is B 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
$=\sqrt{(x_2-x_1{)}^2+(y_2-y_1{)}^2+(z_2-z_1{)}^2}$
$PQ=\sqrt{(1+2{)}^2+(2-3{)}^2+(3-5{)}^2}=\sqrt{14}$
$QR=\sqrt{36+4+16}=\sqrt{56}=2\sqrt{14}$
$PR=\sqrt{(7+2{)}^2+(0-3{)}^2+36}=\sqrt{126}=3\sqrt{14}$
For triangle to form $\text{sum of any two sides > third side}$ But,
Clearly, $PQ+QR=PR$
$\text{Hence P,Q,R are collinear points.}$