Home › Maharashtra HSC (Class 12) › Mathematics › Vectors › Volume of a parallelepiped with edges a, b, c is
Volume of a parallelepiped with edges a, b, c is
Aa · b · c
B|[a b c]|
C|a + b + c|
D(1/6)|[a b c]|
Answer & Solution
Correct answer: B. |[a b c]|
1. The scalar triple product [a b c] = a · (b × c) gives a signed volume.
2. Volume of the parallelepiped is the absolute value of this triple product.
3. Hence the answer is |[a b c]|.
_Source: Maharashtra Balbharati Std XII Mathematics Part 1, Ch 5 "Vectors" §5.6_
Related questions
Vector $PQ$ has magnitude 5 units and is inclined at $150^{\circ}$ to the $x$-axis. In theForces $2i-5j+6k$ and $-i-2j-k$ move a particle from $A(4,-3,-2)$ to $B(6,-1,-3)$. The worPosition vectors $2i-j+k$, $i-3j-5k$ and $3i-4j-4k$ form a triangle with sides $ qrt{41}$,When are two vectors counted as equal?What is the magnitude of the position vector with components 9 and 12?Which two features identify a vector?The work done by a constant force F in displacement d isIf a, b, c are mutually perpendicular unit vectors, the value of a · (b × c) is