Obtain a unit vector perpendicularto both ˆ ˆA 5 3i j→= + and→= − − +ˆ ˆ ˆB 2i j k

To obtain a unit vector perpendicular to both vector A (5i + 3j) and vector B (-2i - j + k), we can follow these steps:

1. Calculate the cross product of vector A and vector B. The cross product is given by the formula: A x B = (AyBz - AzBy)i + (AzBx - AxBz)j + (AxBy - AyBx)k.

   Plugging in the values, we have: A x B = (3*(-1) - 0*(-2))i + (0*(-1) - 5*(-2))j + (5*(-1) - 3*(-2))k = (-3)i + (10)j + (-7)k

2. Normalize the resulting vector to obtain a unit vector. The normalization process involves dividing each component of the vector by its magnitude.

   The magnitude of the resulting vector is given by the formula: |A x B| = sqrt((-3)^2 + (10)^2 + (-7)^2) = sqrt(9 + 100 + 49) = sqrt(158) ≈ 12.57.

   Dividing each component of the resulting vector by its magnitude, we get: Unit vector = (-3/12.57)i + (10/12.57)j + (-7/12.57)k

Therefore, the unit vector perpendicular to both vector A and vector B is approximately (-0.24)i + (0.80)j + (-0.56)k.