Find a unit vector that is orthogonal to both →u= ⟨6,−3,−8⟩ and v= ⟨−7,10,0⟩.

Question

Note: This question is very sensitive to rounding errors. Enter an exact answer only.

Answer 1

Find a unit vector that is orthogonal to both →u= ⟨6,−3,−8⟩ and v= ⟨−7,10,0⟩.

n = u x v = ⟨6,−3,−8⟩ x ⟨−7,10,0⟩ = < 80 , −56 , 39 > is a vector orthogonal to both u and v.

Then a unit vector w = n / || n || = < 80 , −56 , 39 > 1 / √( 80² + 56² + 39²) = [1/ √ 11057 ] < 80 , −56 , 39 >

Answer 2

uXv is a vector perpendicular to both u and v.

| i j k |

| 6 -3 -8 |

| -7 10 0 |

No way to write a determinant. i j k first row 6,-3,-8 second row, -7 10 0 third row

80i+56j+39k is the determinant. The vector is perpendicular t both u and v