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# notes001 (43) - MATH 2203&Quiz 2(Version 2 Solutions...

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Unformatted text preview: MATH 2203 &Quiz 2 (Version 2) Solutions September 3, 2010 NAME_______________________________ 1) Let u = & i & 4 j & 2 k and v = & 5 i + 3 j . Compute u Â¡ v (using any method that you want &but you must show the details). Solution: u Â¡ v = & & & & & & i j k & 1 & 4 & 2 & 5 3 & & & & & & = & & & & & 4 & 2 3 & & & & i & & & & & & 1 & 2 & 5 & & & & j + & & & & & 1 & 4 & 5 3 & & & & k = 6 i + 10 j & 23 k . 2) Show that u Â¡ v (which you computed in problem 1) is orthogonal to both u and v . Solution: ( u Â¡ v ) Â¢ u = (6 i + 10 j & 23 k ) Â¢ ( & i & 4 j & 2 k ) = (6) ( & 1) + (10) ( & 4) + ( & 23) ( & 2) = 0 and ( u Â¡ v ) Â¢ v = (6 i + 10 j & 23 k ) Â¢ ( & 5 i + 3 j ) = (6) ( & 5) + (10) (3) + ( & 23) (0) = 0 so u Â¡ v is orthogonal to both u and v . 3) Find either parametric equations or symmetric equations for the line that contains the point P (5 ; 4 ; & 2) and is parallel to the vector v = h 1 ; & 2 ; & 5 i ....
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notes001 (43) - MATH 2203&Quiz 2(Version 2 Solutions...

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