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

Find the area of the parallelogram whose adjacent sides are A=3 i+ j+2 k and B= i- j+2 k.

1. 48 sq. units
2. 9.17 sq. units
3. 6.93 sq. units
4. 4 sq. units

Answer

C. 6.93 sq. units

Solution

A× B= vmatrix i& j& k\3&1&2\1&-1&2 vmatrix=4 i-4 j-4 k. The area is | A× B|=sqrt(16+16+16)=4 3 6.93.

More Vector Algebra: Dot and Cross Products questions

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

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