Question

Assertion :The points $(2,1,5)$ and $(3,4,3)$ lie on opposite sides of the plane $2x+2y-2z-1=0$ Reason: The algebraic perpendicular distance from the given points to line have opposite signs.

• A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
• B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
• C. Assertion is correct but Reason is incorrect
• D. Both Assertion and Reason are incorrect

Answer 1

The correct option is A Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

Perpendicular distance of a point $P(x_{\circ },y_{\circ },z_{\circ })$ from the plane $ax+by+cz+d=0$ is $\frac{a{x}_{\circ }+b{y}_{\circ }+c{z}_{\circ }+d}{\sqrt{a^2+b^2+c^2}}$

Equation of line is $2x+2y-2z-1=0$

For point $(2,5,1)$

Distance$=\frac{2\times 2+2\times 1-2\times 5-1}{\sqrt{2^2+2^2+2^2}}=\frac{4+2-10-1}{2\sqrt{3}}=\frac{-5}{2\sqrt{3}}$

For point $(3,4,3)$

Distance$=\frac{2\times 3+2\times 4-2\times 3-1}{\sqrt{2^2+2^2+2^2}}=\frac{8-1}{2\sqrt{3}}=\frac{7}{2\sqrt{3}}$

Since the distance of both points are opposite in signs positive points lie on either side of the plane.

Hence, we can see that reason given is correct. Therefore both assertion and reason are correct and reason is the correct explanation of assertion.