If $A \cdot \mathrm{adj}(A) = O$, then $|A|$ is}

Question

Let the foot of the perpendicular from the point $ (1, 2, 4) $ on the line $ \frac{x+2}{4} = \frac{y-1}{2} = \frac{z+1}{3} $ be $ P $. Then the distance of $ P $ from the plane $ 3x + 4y + 12z + 23 = 0 $ is:

Answer 1

Step 1: Conceptual Understanding:
Use the standard identity $A \cdot \mathrm{adj}(A) = |A|\,I$.
Step 2: Explanation in Detail:
$A \cdot \mathrm{adj}(A) = |A|\,I = O \Rightarrow |A| = 0$.
Step 3: Therefore, Stating the Final Answer
$|A| = 0$.

If $A \cdot \mathrm{adj}(A) = O$, then $|A|$ is}

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The Correct Option is A

Solution and Explanation

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