Question

Assertion :If $ax+by+cz=\sqrt{a^2+b^2+c^2}$ be a plane and $(x_1,y_1,z_1)$ and $(x_2,y_2,z_2)$ be two points on this plane then $a(x_1-x_2)+b(y_1-y_2)+c(z_1-z_2)=0$ Reason: If two vectors $p_1\hat{i}+p_2\hat{j}+p_3\hat{k}$ and $q_1\hat{i}+q_2\hat{j}+p_3\hat{k}$ are orthogonal then $p_1{q}_1+p_2{q}_2+p_3{q}_3=0$

• 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 A Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

Given Assertion is that If $ax+by+cz=\sqrt{a^2+b^2+c^2}$ be a plane

and $(x_1,y_1,z_1)$ and $(x_2,y_2,z_2)$ be two points on this plane

then $a(x_1-x_2)+b(y_1-y_2)+c(z_1-z_2)=0$

$\therefore$ Assertion is correct

If two vectors $p_1\hat{i}+p_2\hat{j}+p_3\hat{k}$ and $q_1\hat{i}+q_2\hat{j}+p_3\hat{k}$ are orthogonal

$\therefore p_1{q}_1+p_2{q}_2+p_3{q}_3=0$

Hence Reason also correct

$\therefore$ Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.