Exam1.BlueSol

# Exam1.BlueSol - MATH 32A EXAM I OCTOBER 19, 2009 LAST NAME...

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MATH 32A EXAM I OCTOBER 19, 2009 LAST NAME FIRST NAME ID NO. WRITE CLEARLY AND LEGIBLY. TO RECEIVE CREDIT, YOU MUST CIRCLE YOUR ANSWERS . PLEASE DO NOT WRITE BELOW THIS LINE SCORES 1( 2 0p o i n t s ) 5( 2 o i n t s ) 2( 2 o i n t s ) 6( 2 o i n t s ) 3( 2 o i n t s ) 7( 2 o i n t s ) 4( 2 o i n t s ) TOTAL

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2 PROBLEM 1 Let v = h 1 , 1 , 1 i . Write the vector w = h 3 , 2 , 1 i as a sum w = w || + w where w || is parallel to v and w is perpendicular to v . Solution: We have w || = ± v · w v · v ² v = ³ h 1 , 1 , 1 i·h 1 , 2 , 3 i h 1 , 1 , 1 1 , 1 , 1 i ´ h 1 , 1 , 1 i = h 2 , 2 , 2 i and w = w w || = h 3 , 2 , 1 i−h 2 , 2 , 2 i = h 1 , 0 , 1 i The decomposition with respect to v is w = h 3 , 2 , 1 i = h 2 , 2 , 2 i + h 1 , 0 , 1 i
3 PROBLEM 2 Two vectors v and w (based at the origin) of length 8 lie in the plane 2 x +3 y 4 z =0 The angle between v and w is θ = π/ 6. With this information you can determine the cross product v × w up to a sign. Find a vector u such that v × w = ± u .

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## This note was uploaded on 10/26/2011 for the course MATH 32A taught by Professor Gangliu during the Spring '08 term at UCLA.

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Exam1.BlueSol - MATH 32A EXAM I OCTOBER 19, 2009 LAST NAME...

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