Find a vector of magnitude 6, which is perpendicular to both the vectors 2 i - j+2 k and 4 i - j+3 k


Let the vectors be and , such that



We need to find a vector perpendicular to both the vectors and .


Any vector perpendicular to both and can be given as,






Let



As we know, a unit vector in a normed vector space is a vector (often a spatial vector) of length 1.


So,


A vector of magnitude 6 in the direction of is given by,




Here, .








Thus, required vector is .


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