Question

Calculate the volume of a parallelepiped with sides give as

a
=
(
7,2
,
4
)
,
b
=
(
4,7
,
6
)
and
c
=
(
3,4
,
7
)

Select one:

105
cubic units


125
cubic units


115
cubic units


135
cubic units

Answer 1

To calculate the volume of a parallelepiped given the sides, we can use the scalar triple product. The formula for the volume of a parallelepiped with sides a, b, and c is:

Volume = |a · (b × c)|

where · represents the dot product and × represents the cross product.

Using the given sides:

a = (7, 2, 4)

b = (4, 7, 6)

c = (3, 4, 7)

First, calculate the cross product of b and c:

b × c = (7*7 - 4*4, 6*3 - 7*7, 4*4 - 2*3)

= (49 - 16, 18 - 49, 16 - 6)

= (33, -31, 10)

Next, calculate the dot product of a and the cross product (b × c):

a · (b × c) = 7*33 + 2*(-31) + 4*10

= 231 - 62 + 40

= 209

Finally, take the absolute value of the result to obtain the volume:

Volume = |209| = 209 cubic units

Therefore, the correct answer is:

209 cubic units