Question

Assertion :The equation $3x^2-9y^2+6z^2+4yz-2zx+xy=0$ represent a pair of $\perp$ er planes. Reason: A pair of planes given by $a{x}^2+b{y}^2+c{z}^2+2fyz+2gzx+2hxy=0$ are $\perp$ er if $a+b+c=0$

• 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

$3x^2-9y^2+6z^2+4yz-2zx+xy=0$
$\therefore a=3,b=-9,c=6,f=2,g=-1,h=\frac{1}{2}$
$\therefore a+b+c=0$

$3-9+6=0$
$\therefore$ Given equation does represent a pair of planes perpendicular to each other.
$\therefore$ Assertion (A) is true and the other hand the Reason (R) is obvious