Question

Assertion :Points $A(4,0,4),B(1,2,3),C(-2,4,2)$ are collinear Reason: Three points $A,B,C$ are collinear if $AB+BC=AC$ and $AB,BC<AC$

• A. Both Assertion & Reason are individually true & Reason is correct explanation of Assertion
• B. Both Assertion & Reason are individually true but Reason is not the ,correct (proper) explanation of Assertion
• C. Assertion is true but Reason is false
• D. Assertion is false but Reason is true

Answer 1

The correct option is A Both Assertion & Reason are individually true & Reason is correct explanation of Assertion

Points A(4,0,4),B(1,2,3),C(−2,4,2) are collinear

formula to check whether these three points are collinear or not

AB+BC=AC

to find AB the equation is

$\sqrt{(x_2-x_1{)}^2+(y_2-y_1{)}^2+(z_2-z_1{)}^2}$ ---(1)

$x_1=4,y_1=0and{z}_1=4$

$x_2=1,y_2=2and{z}_2=3$

by substituting the values in (1) we will get

AB = 3.7

similarly for BC and AC

BC=3.7

AC=7.4

hence finally its is known that these points are collinear

the answer will be Both Assertion & Reason are individually true & Reason is correct explanation of Assertion.