The volume of the parallelopiped whose sides are given by , , , is
- A.
- B.
- C.
- D.None of these
Show answer and solution
Correct option: B
Solution
The volume equals |[OA, OB, OC]|, the absolute value of the scalar triple product.
Scalar triple product = OA · (OB × OC)
Compute as the determinant:
|2 -3 0|
|1 1 -1|
|3 0 -1|
= 2[(1)(−1) − (−1)(0)] − (−3)[(1)(−1) − (−1)(3)] + 0
= 2[−1 − 0] + 3[−1 + 3]
= 2(−1) + 3(2)
= −2 + 6 = 4
Volume = |4| = 4.
Scalar triple product = OA · (OB × OC)
Compute as the determinant:
|2 -3 0|
|1 1 -1|
|3 0 -1|
= 2[(1)(−1) − (−1)(0)] − (−3)[(1)(−1) − (−1)(3)] + 0
= 2[−1 − 0] + 3[−1 + 3]
= 2(−1) + 3(2)
= −2 + 6 = 4
Volume = |4| = 4.
[1983]