# Find all values of a so that u and v are orthogonal

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Find all values of a so that u and v are orthogonal. (Enter your answers as a comma-separated list.) Solution or Explanation || 2 u 3 u 8 || = ( 2 ) = = 1 1 ( 3 ) 2 + 1 2 + ( 1) 2 11 ||4 u 2 ( 2 u 6 )|| = 4 ( 2) = = = 1 1 1 0 3 1 4 10 2 4 2 + ( 10 ) 2 + 2 2 120 30 = 2 0 1 1 3 3 1 = 2 u = , v = 1 2 a 0 2 1 a 6 a = (No Response)
u · v = · = (1)( 2 ) + ( 2 )(1) + a ( a ) + 0( 6 ) = a 2 4 a = ± 2 . 1 2 a 0 2 1 a 6
3. –/3 pointsHoltLinAlg1 8.1.019. Find all values of a and b (if any) so that the given vectors form an orthogonal set. (If an answer does not exist, enter DNE.) Solution or Explanation and Hence we obtain the system Solving, we obtain and 4. –/3 pointsHoltLinAlg1 8.1.026. Suppose that u 1 and u 2 are orthogonal vectors, with and Find Solution or Explanation u 1 = , u 2 = , u 3 = 2 1 1 3 4 2 2 a b ( a , b ) = (No Response) u 1 · u 2 = · = 0, 2 1 1 3 4 2 u 1 · u 3 = · = a b + 4 , 2 1 1 2 a b u 2 · u 3 = · = 4 a + 2 b + 6 . 3 4 2 2 a b a b + 4 = 0 4 a + 2 b + 6 = 0. a = 7 b = 11 . u 1 = 5 u 2 = 2 . 4 u 1 u 2 . 4 u 1 u 2 = (No Response) 4 u 1 u 2 = = = = = 2 . 4 u 1 + u 2 2 2 ( 4 u 1 ) 2 + ( u 2 ) 2 ( 4 ( 5 )) 2 + ( 2 ) 2 404 101