Engineering Board Exam Reviewer · Vector Algebra: Dot and Cross Products · medium

Find the volume of the parallelepiped with edges A= i+2 k, B=3 j+ k, and C=2 i+ j.

1. 13
2. -13
3. 11
4. 5

Answer

A. 13

Solution

The volume is | A·( B× C)|, the absolute value of vmatrix1&0&2\0&3&1\2&1&0 vmatrix=1(0-1)-0+2(0-6)=-13. The volume is 13 cubic units.

More Vector Algebra: Dot and Cross Products questions

1. Find the scalar projection of A=3 i+4 j onto B= i+2 j+2 k.
2. Find the area of the parallelogram whose adjacent sides are A=3 i+ j+2 k and B= i- j+2 k.
3. Find the angle between A= i+2 j+2 k and B=2 i- j+2 k.
4. Find A× B if A= i + 2, j + 3, k and B=2, i - j + k.
5. Find the magnitude of A=2 i-2 j+ k.
6. Find A· B if A=2, i + 3, j - k and B= i - 2, j + 4, k.
7. Find a unit vector perpendicular to both A=2 i- j+ k and B= i+2 j- k.

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