Vector Algebra: Dot and Cross Products — Engineering Board Exam Practice Questions

8 free engineering board exam reviewer questions on Vector Algebra: Dot and Cross Products (Advanced Engineering Mathematics), each with the correct answer and a worked solution.

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