60 units cubed.
The volume of the parallelepiped is the absolute value of the scalar triple product, so in this case it's the absolute value of
which is positive, so the volume is 60 units cubed.
In this case the vectors are all orthogonal to each other so this is a rectangular prism with sides 3, 4, and 5, so the volume is lengthwidthheight, which again gives 60 units cubed.
parallelepiped is what you get when you make a cuboid with parallelograms instead of rectangles.
This might go long !
Speaking geometrically , the volume of the parallelepiped is similar to that of a cuboid (cube is also a cuboid made of perfect rectangles , i.e , squares). Its the product of length , width and height .
See the image above . If it were a cuboid , the volume would be
bca . But this is not the case in parallel-boid (that's made up for sure ! ) . Do you notice how i said volume = length * width * height?
What height means is the perpendicular distance between the base and opposite face , that is marked 'h' in the picture above.
Also note that
Now using the three vectors given , you can compute the box product (also known as triple product).
The notation is [a,b,c] . The operation is
I am skipping the calculation hoping you know how to calculate dot products and cross products .
The final answer is
Hope this helps!