Question

find the volume of parallelepiped if a=[3,4,0] b= [2,3,4] and c=[0,0,5] are its edges​

Answer 1

$\textbf{Given:}$

$\text{Edges of the parallelopiped are a=[3,4,0],\;b=[2,3,4], and c=[0,0,5] }$

$\textbf{To find:}$

$\text{Volume of the parallelopiped having coterminus edges a,b and c }$

$\textbf{Solution:}$

$\text{We know that, volume of the parallelopiped having coterminus edges a,b and c is [a\,b\,c] }$

$[a\,b\,c]$

$=\text{Scalar triple product of a,b and c }$

$=\left|\begin{array}{ccc}3&4&0\\2&3&4\\0&0&5\end{array}\right|$

$\text{Expanding along first row, we get}$

$=3(15-0)-4(10-0)+0$

$=3(15)-4(10)$

$=45-40$

$=5\;\text{cubic units}$

$\textbf{Answer:}$

$\boxed{\textbf{Volume of the given paraelopiped is 5 cubic units}}$

Answer 2

Step-by-step explanation:

Given find the volume of parallelepiped if a=[3,4,0] b= [2,3,4] and c=[0,0,5] are its edges

• Now we have the triple scalar product. So we get
• So a = (3,4,0), b = (2,3,4) and c = (0,0,5) are the edges.
• So a.(b x c) =      3   4   0    
•                            2   3   4
•                            0   0   5
•                  = 3   3   4     - 4   2   4    + 0   2    3    
•                           0   5           0    5            0    0
•                = 3(15 + 0) – 4(10 – 0) + 0 (0 – 0)
•               = 3(15) – 4(10)
•                = 45 – 40
•                  = 5
• So volume of parallelopiped is 5 cubic units.

Reference link will be

https://brainly.in/question/18946090