Question

Assertion :$ABCD{A}_1{B}_1{C}_1{V}_1$ is a cube edge 1 unit, P and Q are the mid points of the edges $B_1{A}_1$ and $B_1{C}_1$ respectively. Then the distance of the vertex D from the plane PBQ is $\frac{8}{3}$ Reason: Perependicular distance of point $(x_1,y_1,z_1)$ from the plane $ax+by+cz+d=0$ is given by $\left|\frac{a{x}_1+b{y}_1+c{z}_1+d}{\sqrt{a^2+b^2+c^2}}\right|$

• 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. Assertion is incorrect but Reason is correct

Answer 1

The correct option is D Assertion is incorrect but Reason is correct

Given $ABCD{A}_1{B}_1{C}_1{V}_1$ is a cube edge 1 unit,

P and Q are the mid points of the edges $B_1{A}_1$ and $B_1{C}_1$ respectively.

Then the distance of the vertex D from the plane PBQ is $\frac{8}{3}$

From above Assertion is incorrect

Perependicular distance of point $(x_1,y_1,z_1)$ from the plane $ax+by+cz+d=0$ is

$\left|\frac{a{x}_1+b{y}_1+c{z}_1+d}{\sqrt{a^2+b^2+c^2)}}\right|$

But Reason is correct

Hence Assertion is incorrect but Reason is correct.