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Unformatted text preview: Mathematics 20C Spring 2009 Test 1 Name: Section: ID: Be sure to show all work. Answers without full justification are worth no credit. Remember that you can often check your answers. You may use a single page of notes, but no other aids are allowed. This test consists of 4 questions. Each question is worth a total of 5 points. 1 /5 2 /5 3 /5 4 /5 ∑ /20 1) Let u = ( 2 , 1 , 3 ) and v = (− 1 , s, 2 ) where s is some real number. (2 points) (a) Find what value s must be for u and v to be orthogonal. In order for u and v to be orthogonal, it must be that u · v = 0. This becomes − 2 + s + 6 = 0 or simply s = − 4. (3 points) (b) Using the value for s you found above, find a third vector w negationslash = 0 which is orthogonal to both u and v . In order to find w which is orthogonal to both u and v , we can compute w = u × v = det i j k 2 1 3 − 1 − 4 2 = (2 + 12) i − (4 + 3) j + ( − 8 + 1) k = ( 14 , − 7 , − 7 ) . 2) Let l ( t ) be the line through the points (...
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This note was uploaded on 10/29/2009 for the course MATH Math 20C taught by Professor Lunasin during the Spring '08 term at UCSD.
 Spring '08
 Lunasin
 Math

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