Engineering Board Exam Reviewer · Vector Algebra: Dot and Cross Products · hard
Find a unit vector perpendicular to both A=2 i- j+ k and B= i+2 j- k.
- i+3 j+5 ksqrt(35)
- - i+3 j+5 ksqrt(35)
- - i+3 j+5 k/35
- 3 i+ jsqrt(10)
Answer
B. - i+3 j+5 ksqrt(35)
Solution
A× B= vmatrix i& j& k\2&-1&1\1&2&-1 vmatrix=(1-2) i-(-2-1) j+(4+1) k=- i+3 j+5 k, which is perpendicular to both. Its magnitude is sqrt(1+9+25)=sqrt(35), so the unit vector is - i+3 j+5 ksqrt(35).
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