Determine the unit vector perpendicular to both the vectors A=2i +j+2k ad vector B=i-j+2k
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The unit vector along the given vectors A and B is given by the formula
A × B / Ι A × B Ι
Given vectors are
A = 2i + j +2k
B = i - j + 2k
The cross product of the above two vectors is given as
A × B = (2i + j +2k) × (i - j + 2k)
A × B = 4i - 2j - 3k
Now we calculate Ι A × B Ι
Ι A × B Ι = √(4)² + (-2)² + (-3)²
Ι A × B Ι = √29
Hence unit vector is 4i - 2j - 3k / √29
A × B / Ι A × B Ι
Given vectors are
A = 2i + j +2k
B = i - j + 2k
The cross product of the above two vectors is given as
A × B = (2i + j +2k) × (i - j + 2k)
A × B = 4i - 2j - 3k
Now we calculate Ι A × B Ι
Ι A × B Ι = √(4)² + (-2)² + (-3)²
Ι A × B Ι = √29
Hence unit vector is 4i - 2j - 3k / √29
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