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Let the vectors A = 3i - j + 5k and B = i +2j -3k , determine a vector C knowing that it is perpendicular to the OZ axis and that it verifies the relations

C dot A = 9 and C dot B = 4 .

if C ⊥ OZ then its z component is zero. So C = mi+nj

C•A = 3m-n = 9
C•B = m+2n = 4
solve that to get m and n, and you have
C = 22/7 i + 3/7 j

Did you know?

Did you know that in three-dimensional space, vectors can be perpendicular to different axes? In this case, we are looking for a vector, let's call it C, that is perpendicular to the OZ axis. To find C, we are given two conditions: 1. The dot product of C and A is equal to 9, which is denoted as C dot A = 9. 2. The dot product of C and B is equal to 4, which is denoted as C dot B = 4. By using the dot product formula, we can develop two equations using the given conditions. Next, we can substitute the components of vectors A and B into the equations. By solving these equations simultaneously, we can determine the vector C that is both perpendicular to the OZ axis and satisfies the given relations. This process allows us to explore the relationship between vectors and geometric axes in three-dimensional space.