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Question: What will be the volume of that parallelopiped whose sides are **a** = **i** – **j** + **k**, **b** ...

What will be the volume of that parallelopiped whose sides are a = i – j + k, b = i – 3j + 4k and c = 2i – 5j + 3k

A

5 unit

B

6 unit

C

7 unit

D

8 unit

Answer

7 unit

Explanation

Solution

Volume of parallelopiped=[abc]= \lbrack\mathbf{abc}\rbrack =∣1−111−342−53∣=(−9+20)−(8−3)+(−5+6)=7= \left| \begin{matrix} 1 & - 1 & 1 \\ 1 & - 3 & 4 \\ 2 & - 5 & 3 \end{matrix} \right| = ( - 9 + 20) - (8 - 3) + ( - 5 + 6) = 7unit.