How do you find a unit vector that is orthogonal to a and b where #a = −7 i + 6 j − 8 k# and #b = −5 i + 6 j − 8 k#?
The answer is
To find a vector orthogonal to 2 other vectors, we must do a cross product.
The cross product of 2 vectors,
is given by the determinant
Here, the 2 vectors are
And the cross product is
Verification, by doing the dot product
Therefore, the vector is perpendicular to the other 2 vectors
The unit vector isobtained by dividing by the modulus.
The modulus is
The unit vector is