Find the volume of the parallelepiped formed by (mathbf{a}=(1,,2,,3)), (mathbf{b}=(0,,-2,,1)) and (mathbf{c}=(4,,1,,-1)).
Answer
33
The correct answer is 33 — The volume is the absolute value of this scalar triple product: (|33|=33).
Step-by-step solution
- Compute the cross product (mathbf{b}\times\mathbf{c}): (mathbf{b}\times\mathbf{c}=\begin{vmatrix}mathbf{i}&mathbf{j}&mathbf{k}\0&-2&1\4&1&-1end{vmatrix}=(1,,4,,8)).
- Take the dot product of (mathbf{a}) with (mathbf{b}\times\mathbf{c}): (1\times1+2\times4+3\times8=1+8+24=33).
- The volume is the absolute value of this scalar triple product: (|33|=33).
Common mistake: wrong sign in cross product or forgetting absolute value
Concept tested: scalar triple product
Published · How this solution was prepared and checked
← All Vector Algebra questions