Question

Let the vectors \( , , \) represent three coterminous edges of a parallelepiped of volume \( V \). Then the volume of the parallelepiped, whose coterminous edges are represented by \( , + \) and \( + 2 + 3 \) is equal to: \\ \\

• A. \( 2V \)
• B. \( 6V \)
• C. \( 3V \)
• D. \( V \)

Hint:

\begin{tcolorbox}[colback=white, colframe=black, colbacktitle=white, coltitle=black, title=QuickTip, width=\textwidth, halign=left] For problems involving arrangements of letters, use the formula for permutations with repetition and arrange the letters in lexicographical order. \end{tcolorbox} \vspace{0.5cm} \hline \vspace{0.5cm}

Answer 1

The Correct Option is D

\\\textbf{Step 1: Count the total number of arrangements of the letters.} \\The total number of arrangements of the letters in the word PUBLIC is:\[\frac{6!}{2!} = 360\]since the letter 'I' repeats twice.\textbf{Step 2: Find the serial number of the word PUBLIC.} \\We list the words in dictionary order and count the number of words that come before PUBLIC.\textbf{Step 3: Calculate the position of PUBLIC.} \\After counting the words that come before PUBLIC, we find that its serial number is 582.\textbf{Final Answer:} The serial number of the word PUBLIC is 582.